The FBI has spent years trying to repair damage done by its zealous pursuit of former President Donald Trump — and then Director Christopher Wray reopened the wounds by suggesting that Mr. Trump wasn’t actually struck by a would-be assassin’s bullet.

Mr. Wray twice suggested in testimony to Congress last week that “shrapnel” may have bloodied the former president’s right ear.

Initially defiant, the FBI backtracked on that suggestion Friday night.

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“What struck former President Trump in the ear was a bullet, whether whole or fragmented into smaller pieces, fired from the deceased subject’s rifle,” the bureau said in an unattributed statement from its press office.

But the damage was done.

“It’s disappointing but not surprising that the same FBI that’s spent the last eight years targeting President Trump would engage in this kind of baseless conspiracy mongering,” said Rep. Tom Tiffany, Wisconsin Republican.

Mr. Wray’s assessment contradicted the victim himself, the emergency room doctors who treated Mr. Trump, his former White House physician who has been tracking the case and even The New York Times, which conducted an analysis of photos and audio and concluded the gunman’s first bullet grazed the former president’s right ear.

In the initial reporting on the shooting, some accounts said the former president was struck by flying glass, perhaps from a teleprompter. Mr. Trump, though, quickly took to social media to say it was a bullet that hit him.

He has said the bullet could have killed him if his head had been turned a quarter of an inch further.

Thomas J. Baker, who was the first FBI agent on the scene of President Ronald Reagan’s shooting in 1981, called Mr. Wray’s foray into the bullet-shrapnel issue “puzzling.”

“His throwing out that doubt about this — that question should have been resolved at the crime scene within hours,” said Mr. Baker, author of “The Fall of the FBI.”

He said Mr. Trump should have been one of the early interviews the FBI did because he’s a “victim-witness” of the July 13 shooting.

Mr. Wray chose a poor time to seem to pick a fight with the former president’s version of events.

As Congress held hearings this week on the assassination attempt, Republicans denounced the FBI for lacking credibility.

“We have no confidence in the FBI,” House Oversight and Accountability Chairman James Comer said as he opened the first hearing with Kimberly Cheatle, who at the time was Secret Service director.

Ms. Cheatle resigned that post a day after her disastrous performance at the hearing.

Mr. Wray showed up on Capitol Hill determined to do better. Where Ms. Cheatle waffled and demurred, Mr. Wray promised to be as open as possible, even in areas where his investigation is still open.

He offered lawmakers a few juicy new tidbits, such as the multiple visits the shooter made to the rally site beforehand, his use of a drain pipe to get to his rooftop sniper’s perch and his purchase of ammunition the day of the shooting.

But twice during the lengthy hearing Mr. Wray, responding to questions asking about a bullet that struck Mr. Trump, cast doubt.

“With respect to former President Trump there’s some question about whether or not it’s a bullet or shrapnel that, you know, that hit his ear,” Mr. Wray said in response to a question from Chairman Jim Jordan, Ohio Republican.

That was news to Rep. Ronny Jackson, who served as White House physician for 14 years, including for Mr. Trump. The Texas Republican has visited with Mr. Trump since the shooting and said he’s been keeping tabs on the medical case and said the ear injury has all the markings of a bullet wound.

“There is absolutely no evidence that it was anything other than a bullet,” Mr. Jackson said on social media. “Director Wray is wrong and inappropriate to suggest anything else.”

He pointed out that was the conclusion of the emergency room doctors, who labeled the injury a “gunshot wound” in their report.

Meanwhile, The New York Times last week said it conducted an analysis of photos and audio and bullet trajectories and concluded he was grazed by the first shot taken by the gunman.

Other bullets killed one rally-goer and critically wounded two others.

The FBI and Mr. Trump have tangled for years, dating back to the 2016 election when the bureau wiretapped a Trump campaign adviser and pursued a now-discredited investigation into a Trump-Russia conspiracy.

An inspector general said the FBI’s investigation was inappropriate.

Mr. Trump in 2017 fired Director James B. Comey, which helped spark a Justice Department special counsel probe. That probe faulted Mr. Trump for the firing, but found no evidence of the Russia-Trump conspiracy.

In 2020, the FBI knew the Hunter Biden laptop was authentic but kept silent as the Biden campaign organized an effort to discredit the laptop as Russian disinformation.

At Wednesday’s hearing, Mr. Wray acknowledged lingering issues to Mr. Tiffany, who pointed out an FBI contractor had drafted a questionnaire form — apparently for conducting an internal investigation of a bureau employee — that probed “support for President Trump” and “objection” to the coronavirus vaccination as worrying indicators.

Mr. Wray said the form was “completely inappropriate.” He said the contractor is “no longer affiliated with the FBI” and he has alerted the Justice Department inspector general to the incident.