Washington (CNN) When Chief Justice John Roberts rebuked President Donald Trump over judicial independence in November, some critics countered with a 2010 moment between President Barack Obama and Justice Samuel Alito.

That instantly viral episode, with Alito mouthing "not true," as Obama disparaged the Citizens United campaign finance decision during a State of the Union address, was not quite comparable.

But it did again put a rare spotlight on one of the Supreme Court's least known but most important justices -- as did his pungent questioning in oral arguments this week.

As a lawyer faltered in the face of one of Alito's distinctive hypothetical questions on Thursday, Alito insisted, against his reputation as a tough interlocutor on the bench: "I don't think this is a surprise question, or a particularly difficult one."

Through his opinions, Alito, who succeeded centrist Justice Sandra Day O'Connor in 2006, has moved the court to the right on reproductive rights, religious freedom, job discrimination and campaign finance regulations.

Since the February 2016 death Justice Antonin Scalia, Alito has anchored the right wing of the nation's high court with Justice Clarence Thomas. The addition of Trump appointees Justice Neil Gorsuch, in 2017, and Brett Kavanaugh in October, could bolster in upcoming years Alito's unflinching conservatism -- to further restrict abortion rights, for example, and to continue last session's support of the Trump administration legal agenda.

The New Jersey native with a caustic wit who still draws attention for his grimaces, rolled eyes and other expressions, stands out as a quirky, somewhat awkward figure among his colleagues on the right and the left. President George W. Bush, who appointed him, wrote in his 2010 memoir about loosening up Alito, a lifelong Phillies fan, with talk of baseball. At a welcome dinner at the court, the other justices even arranged for an appearance by the Phillie Phanatic mascot.

More critically for the law, Alito has written some of the court's most substantial and controversial, opinions, from the 2007 Lilly Ledbetter pay-discrimination case to last term's labor union dispute. The latter reversed a 40-year-old precedent that had permitted public employee unions to charge non-members fees for collective bargaining activities.

Alito's approach to the law has put him on the rightward flank of the court, alongside justices Thomas and Neil Gorsuch. The threesome, for example, recently sought to block a US district court trial over the Department of Commerce's decision to add a citizenship question to the 2020 Census. (The court majority let the trial continue, and the court later said it would hear an appeal on a related evidentiary question in February.)

Thirteen years ago, when President George W. Bush nominated Alito for the O'Connor seat, law professors and legal experts speculated about how far the court might turn to the right -- not unlike the current situation as Kavanaugh has succeeded the moderate conservative Justice Anthony Kennedy.

With Alito, those predictions immediately turned to reality. One year after his appointment, for example, the justices reversed course on an abortion controversy, upholding by a 5-4 vote a federal ban on a late-term procedure that critics called "partial birth." In an earlier case, while O'Connor was still on the bench, the justices had struck down a similar state ban as interfering with a woman's right to end a pregnancy. (Some medical experts said the procedure, known medically as intact dilation and extraction, was the safest for women in certain circumstances.)

Alito has similarly made a difference in religion cases with votes and opinions that would allow more religious expression in public. In a 2014 case, he was in the five-justice majority to uphold Christian prayers before council meetings in Greece, New York, and then wrote a separate concurring statement further defending legislative opening prayers and rejecting a key objection of the four dissenters as "really quite niggling."

In a separate 5-4 case in 2014, combining religious interests and reproductive rights, Alito wrote the court's opinion to allow the Hobby Lobby craft chain and other Christian-run for-profit corporations to escape an Obama administration rule that their insurance cover contraceptives. The regulation arose from the 2010 Affordable Care Act.

Based on his past record, he could play a key role this term in dispute over a World War I Memorial cross on public land in Maryland, challenged as a breach of the constitutional separation of church and state.

The Trump administration has been urging judges to rein in federal regulations, for example on the environment, and Alito has long joined in some conservative skepticism for agency regulations. Yet, he has also chastised his colleagues for chipping away at -- but not directly confronting -- a 1984 court precedent, Chevron v. Natural Resources Defense Council, that says judges should defer to agency interpretation of their legal power.

"In recent years, several members of this court have questioned Chevron's foundations," he wrote in a June dissent . "But unless the court has overruled Chevron in a secret decision that has somehow escaped my attention, it remains good law."

Setting traps at oral arguments

On the bench, Alito stands out with his sharp, methodical approach to questioning lawyers during oral arguments. His queries often involve layered hypothetical questions that can trap advocates.

That happened earlier this year in a controversy over a Minnesota law that prohibited people from wearing any T-shirts or other clothing with a political insignia inside polling places on Election Day.

A group called the Minnesota Voters Alliance challenged the ban on First Amendment grounds, and as the justices pressed the state lawyer defending the prohibition's breadth, Alito said, "The problem is that so many things have political connotations, and the connotations are in the eye of the beholder. ... It's an invitation for arbitrary enforcement."

The attorney defending the state prohibition insisted that it covered items that are "clearly political."

"A shirt with a rainbow flag?" Alito asked, eliciting a hesitant, "yes, unless there was an issue on the ballot that related somehow to gay rights." Then Alito asked about a shirt that bearing the phrase "Parkland Strong," a reference to February's high school shooting in Florida that left 17 people dead. The state lawyer said he thought that would be allowed.

Alito persisted, "Even though gun control would very likely be an issue? ... How about an NRA shirt? ... How about a shirt with the text of the Second Amendment? ... How about the First Amendment?"

The Supreme Court ended up striking down the prohibition on a 7-2 vote as a violation of the First Amendment's free speech guarantee.

In a case Thursday testing a longstanding "separate sovereigns" exception to the Constitution's double jeopardy clause, Alito was skeptical of a lawyer's assertion that the original understanding of the Constitution would forbid dual prosecutions for the same offense.

"So, today," Alito began, "let's say a group of American tourists are murdered by terrorists in a foreign country, and there is a prosecution in the foreign country for murder ... and it's not a sham prosecution, but it's a fairly inept prosecution, lack of prosecutorial investigative resources in a poor country, and it results in an acquittal or a conviction with a very light sentence. And your position is that there could not be a prosecution here in the United States under the statute enacted by Congress to permit the prosecution of individuals who murder Americans abroad?"

"So let me address that in a few different ways.... " the lawyer began.

"Could you just answer whether that's correct or not?" Alito rejoined, as the arguments continued, and the lawyer appeared unable to draw majority support for his position that separate sovereigns -- typically the US government and a state -- should not be able to prosecute a person for the same offense.

'Not true' still reverberates

After Trump last month criticized a US district judge's action in an asylum case and referred to the judge as an "Obama judge," Chief Justice Roberts issued a statement that said: "We do not have Obama judges or Trump judges, Bush judges or Clinton judges. What we have is an extraordinary group of dedicated judges doing their level best to do equal right to those appearing before them."

That led the Republican chairman of the Senate Judiciary Committee, Chuck Grassley, to respond by bringing up the Obama-Alito incident from 2010.

"Chief Justice Roberts rebuked Trump for a comment he made abt judge's decision on asylum I don't recall the Chief attacking Obama when that Prez rebuked Alito during a State of the Union," Grassley tweeted.

Chief Justice Roberts rebuked Trump for a comment he made abt judge's decision on asylum I don't recall the Chief attacking Obama when that Prez rebuked Alito during a State of the Union — ChuckGrassley (@ChuckGrassley) November 21, 2018

But that's not exactly what happened.

The controversy began with the Supreme Court's 5-4 decision on January 21, 2010, striking down federal regulations on corporate and labor union spending in elections, based on the First Amendment. On January 27, at a State of the Union address, Obama disparaged the ruling and referred at one point to the opening of "floodgates" to special interests, including "foreign corporations."

As is customary, Supreme Court justices were sitting in the first two rows for the President's address. Caught on national TV coverage, Alito mouthed "not true," likely responding to the fact that the ruling did not cover foreign corporations.

If Obama noticed Alito's expression at the time, he said nothing about it.

Weeks later, Roberts complained in a speech at the University of Alabama about the State of the Union atmosphere, where the justices must remain silent as members of Congress cheer, and sometimes jeer, throughout a President's speech.

On the bench

Three years after that Alito moment, his facial expressions in response to a dissenting opinion by Justice Ruth Bader Ginsburg made headlines.

In the staid courtroom, Alito had just presented the majority's opinion in a pair of cases limiting the reach of federal law against job discrimination based on race or sex. Then as Ginsburg began reading portions of her dissenting opinion from the bench, saying the majority had diluted the force of Title VII of the 1964 Civil Rights Act, Alito shook his head and rolled his eyes.

For his part, Alito declined to comment then and declined an interview request for this story.