Three of the five FBI employees dinged for anti-Trump bias in the inspector general’s report ended up on the special counsel’s investigation into Donald Trump’s presidential campaign, raising still more questions about the team Robert Mueller assembled.

Two of those — FBI lawyer Lisa Page and her paramour, agent Peter Strzok — became known when their vehemently anti-Trump text messages came to light. But the inspector general’s report identifies a third person, labeled “FBI Attorney 2,” who also fired off messages denigrating Mr. Trump and saying, “Viva le resistance.”

None of the three is still on the special counsel’s team. Ms. Page left weeks after the investigation opened, and Mr. Strzok departed after a couple of months when his anti-Trump messages came to light. Attorney 2, identified by Rep. Mark Meadows this week as Kevin Clinesmith, was ousted from the investigation in February after the inspector general found his messages.

Mr. Clinesmith also sent co-workers political jokes about Mr. Trump, including one instant message after the election saying, “I am so stressed about what I could have done differently.”

According to the report, Mr. Clinesmith worked on the 2016 probe into Hillary Clinton’s email use, then worked on the FBI’s original investigation into the Trump campaign and, eventually, with the special counsel’s investigation into Mr. Trump’s presidential campaign.

The inspector general described Mr. Clinesmith as the primary FBI attorney assigned to the Russia investigation when it started in early 2017.

“If FBI Attorney 2 has the bias that he has, sure, it’s problematic,” Mr. Meadows, North Carolina Republican, told The Washington Times.

The special counsel’s office downplayed Mr. Clinesmith’s involvement Wednesday by portraying him more as a bit player, not key for its roster of prosecutors and federal agents. The office said he was never detailed to the special counsel but remained an FBI agent who supported the investigation in an administrative capacity.

“The special counsel’s investigation is being conducted by prosecutors and agents; FBI Attorney 2 was neither,” said Joshua Stueve, a spokesman for the special counsel.

The lawyer told the inspector general that his anti-Trump comments were “personal feelings” about the election.

Mr. Mueller’s investigation has faced questions about the political leanings of his team.

The special counsel’s office said last year that lawyers picked for Mr. Mueller’s team donated more than $60,000 to Democrats. Only one lawyer donated to Republicans and contributed the maximum amount of $2,750. In total, the investigation’s prosecutors donated $19,000 to Hillary Clinton’s 2008 and 2016 political campaigns, according to Mr. Mueller’s office.

Some media outlets say the numbers underestimate the amount of Democratic donations by as much as $12,000. The donation discrepancy further raises the bias accusations lodged against Mr. Mueller’s team, which Mr. Trump has repeatedly highlighted.

Mr. Trump referred to Mueller’s team this month on Twitter as “13 Angry Democrats.” He said there had “never been a group of people on a case so biased or conflicted.”

The inspector general is looking into whether Mr. Strzok’s anti-Trump bias affected the FBI’s original Russia investigation. Inspector General Michael Horowitz said investigators have not been able to rule out the possibility that decisions to focus investigations on Mr. Trump rather than on Mrs. Clinton in October 2016 was a result of Mr. Strzok’s feelings.

All told, the inspector general found five FBI employees who displayed a bias who were involved in the Clinton investigation. Only Ms. Page and Mr. Strzok were named in last week’s 500-page report, but Mr. Meadows identified Mr. Clinesmith and another lawyer, Sally Moyer, during a hearing Tuesday.

There is no indication that Ms. Moyer had a role on the special counsel’s investigation.

All five have been referred for an internal review, and FBI Director Christopher A. Wray has promised bias training for FBI employees to prevent a repeat.

But their early involvement could be a problem for Mr. Mueller. In a footnote to his report, Mr. Horowitz noted that an unrelated 2012 prosecution under the Foreign Corrupt Practices Act was soured by “racy texts” exchanged by two FBI employees and an informant.

The Justice Department even uses that 2012 case in its employee training as an example of what not to say in text messages.

Ms. Page left the FBI in May, but Mr. Strzok and Mr. Clinesmith are still employed there.

Mr. Strzok was reassigned to the agency’s human resources department after he was removed from Mr. Mueller’s team, but he was escorted out of the FBI building last week.

Solomon Wisenberg, a Washington lawyer who served as independent counsel Kenneth W. Starr’s deputy during investigations into President Clinton, said it is rare for people to be removed from a special counsel investigation.

“It is not unheard of to have a person quietly ushered out, but to have two people kicked off for the appearance of bias is very unusual,” he said.

Mr. Wisenberg said he recalled two people leaving on their own during the five years that the Starr investigation ran its course. But Mr. Mueller has forcibly removed two people, Mr. Clinesmith and Mr. Strzok, in less than a year.

“Turnover is unusual because these things are so exciting, who would want to leave?” he said.

Mr. Wisenberg believes Mr. Mueller is an honorable person trying to conduct a fair investigation, but he described some of his hiring as “tone deaf,” given the accusations of bias that have grown after some team members’ social media posts and political donations were disclosed.

“I think [Mueller] should have been more sensitive,” he said. “It’s obvious Mueller didn’t query his people enough, but that’s not grounds for stopping an investigation.”

Lewis Schiliro, a former head of the FBI’s New York office, said the removal of two people from Mr. Mueller’s team is “a black eye” for the venerable bureau.

He said the use of text and instant message is troubling because the messages are part of a written record of biases that could be used in court to undermine their credibility.

“An FBI agent’s job, first and foremost, is to testify in a court of law,” he said. “But as a defense attorney, the first thing I’m going to do is get their messages and social media posts and show how they are biased witnesses.”

Mr. Schiliro said he couldn’t imagine FBI agents being so cavalier about their political opinions during his time with the bureau.

“It’s just an unbelievable situation,” he said of the anti-Trump comments. “Why these people put those comments out there is beyond me.”

But Andrew Leipold, a law professor at the University of Illinois and a former member of Mr. Starr’s team, said the removals of Mr. Strzok and Mr. Clinesmith dispel accusations of bias that have been lodged against the Mueller investigation.

Mr. Trump has been one of the most vocal in accusing Mr. Mueller of running a political inquisition, calling the investigation a “hoax” and “witch hunt.”

“If the investigation was really as biased as some have alleged, would Mueller be removing people who are biased?” Mr. Leipold said.

Ultimately, the Mueller investigation will be judged by the facts and conclusions, not by the apparent biases of two people who left the investigation relatively early in the process, Mr. Leipold said.

“Is it helpful to Mueller? No. But it doesn’t undermine his credibility because we need to see what the facts are and what people say under oath,” he said.