They showed up to cook, spent one week on the job, and then were summoned to a manager’s office early one Saturday morning in April. Their documents were invalid, they were told. They could punch out and leave the premises.

“They said a new rule had started called E-Verify,” Montes said. “That was the reason they fired us.”

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The firings show that Trump’s company has followed through on its promise this year to start using the government’s online system for checking a new hire’s eligibility to work in the United States — a pledge it made in response to revelations that the company relied on undocumented labor.

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The dismissals also show that the Trump Organization’s adoption of E-Verify has led to further shedding of workers, after the company had already purged about 20 undocumented workers this year. All 12 of Trump’s U.S. golf courses are now enrolled in the program, according to the government’s online database of E-Verify users; in December, only three were enrolled.

Espinoza and Montes said an additional 15 undocumented groundskeepers were let go this year at Trump National Golf Club Colts Neck. The Washington Post was not able to independently verify the additional firings at Colts Neck.

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The Trump Organization did not respond to requests for comment for this article. Trump’s son Eric, who is running his father’s company day-to-day, has said the terminations are a tragic consequence of the workers’ use of false documents to get a job and the country’s broken immigration system.

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The Post has been detailing since late last year the Trump Organization’s history of using undocumented labor and has, so far, interviewed 40 such workers fired from their jobs since then.

Some of the fired workers had been employed by the company for years and said that their supervisors knew their papers were false but allowed them to work there, anyway. The company has denied knowledge that any of its workers were undocumented.

As a candidate railing against undocumented immigrants, Trump declared in a 2016 speech in Arizona, “We will ensure that E-Verify is used to the fullest extent possible under existing law, and we will work with Congress to strengthen and expand its use across the country.”

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The same year, Trump told MSNBC host Chris Matthews: “I’m using E-Verify on just about every job. . . . I’m using E-Verify, and I’ll tell you, it works.”

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It was not until this year, however, that all of the company’s U.S. golf courses began using the system, which allows employers to check the names and personal information of new hires against records held by the Social Security Administration and the Department of Homeland Security.

Eric Trump told The Post in January that the Trump Organization used E-Verify at only some of its properties because the program is not required by law in most states, many competitors do not use it and the system is not foolproof.

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Recently, the president has adopted a more skeptical tone about the idea of mandating E-Verify nationwide.

“The one problem is E-Verify is so tough,” Trump told Fox News earlier this week. The White House declined to comment when asked whether Trump was aware that E-Verify had triggered firings at his own company.

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Still, for some, such as farmers, Trump said, “they’re not equipped for E-Verify.”

The stricter immigration standards at Trump’s golf clubs has caused the company to offer higher salaries for some manual labor jobs and rely more heavily on college-age Americans, according to former workers familiar with staffing decisions. The company has also put out a wide range of help-wanted ads this year, calling for groundskeepers, kitchen staff and other workers. Trump’s golf club in Bedminster, N.J., tried to recruit military veterans to its grounds crew on the jobs site recruitmilitary.com.

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“Do you enjoy working outside?” the ad asked. “Do you get satisfaction in contributing to a team?”

Mark Krikorian, director of the Center for Immigration Studies, a group that advocates for reduced immigration levels, supports a mandatory E-Verify system that would require employers to perform E-Verify checks on new hires but not existing employees. He said the Trump club’s firing of the two cooks — who, despite being veterans of the Trump club, were technically rehired for a seasonal job every year — is what the system is designed to do.

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“That’s the point to E-Verify. The point is to weaken the job magnet,” he said.

Krikorian said that the Trump Organization could have made this move earlier, when the president began his campaign with a strident attack on illegal immigration.

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“You’d think, in 2015, they’d say, ‘Let’s go take a look at this and see what our own situation is,’ ” Krikorian said. “But better late than never.”

A former manager at Colts Neck said that, until recently, immigration checks had not seemed a priority for Trump Organization bosses in New York. The company had required reviews of pay disparities between male and female employees — pursuant to a New Jersey law — and background checks for employees dealing with young golfers. Immigration checks did not have the same priority.

“E-Verify was not big,” said the former manager, speaking on the condition of anonymity to preserve relationships in the golf business. “There was not a specific request [to implement it], because I think there was an additional expense.”

The E-Verify system itself is free, but using E-Verify can still add costs for companies, because the process adds extra work for employees and eliminates possible new hires, dragging out the hiring process.

Decades ago, Espinoza, 46, and Montes, 47, were neighbors in the town of Poza Rica de Hidalgo in the Gulf Coast state of Veracruz, Mexico, they said in an interview in Spanish. They are roommates now in a red brick apartment complex in Freehold, N.J., surrounded by other Hispanic immigrants working in restaurants, landscaping, carpentry, and other manual labor jobs.

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Between them, their salary supports eight children in Mexico — plus parents and spouses. Montes said half of his paycheck — he earned $17.25 an hour last year, according to a pay stub — was sent home each month.

Both men, who began as dishwashers in 2012 before learning to cook, were praised by their colleagues. The former manager, whose tenure overlapped with theirs, said: “They were very hard workers. They were very loyal.”

Upon their firings, the two longtime employees were handed a one-page flier saying they could call the Department of Homeland Security if they wanted more information. When the restaurant’s chef asked Espinoza if he could get his documents in order, Espinoza was shocked.

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“I said, ‘How?’ he recalled saying. “We’ve always told you these weren’t real papers. We’ve always told you the truth. You knew that.’ ”

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The supervisor did not respond to a request for comment.

Espinoza and Montes said they valued their job but routinely felt discriminated against because they could not speak English well and didn’t have legal authorization to work for Trump.

“It enrages you,” Espinoza said. “To hear [Trump] talking about Mexicans, and he had us working there, and he knows how much he exploits Mexicans.”

They said they didn’t receive health insurance, vacation or other benefits that authorized colleagues received.

“I worked sick, with fevers, with headaches, with stomach pain,” Montes said. “I had to keep working. I couldn’t lose a day. I had to pay my rent and my bills.”

Several undocumented workers at other Trump golf courses have also said they were denied these same benefits.