Could the House Republican effort to clear President Trump’s second impeachment from the legal record end up harming his prospects in the courts? That’s a question as some in the House push to “expunge” the accusation from the books.

The Republican démarche is raising criticism from one Democratic congressman that the GOP members are acting as Mr. Trump’s “taxpayer-funded lawyers.” Yet their legal aid could end up resurrecting constitutional questions over Mr. Trump’s acquittal in the Senate on the charge of “incitement of insurrection.”

That’s because the fact that he was charged and acquitted makes it harder for courts to try him again on charges related to the January 6, 2021, attack on the Capitol, for which the courts have tried others. 

This arises from the phrasing in Article I, Section 3 of the Constitution that if a party is impeached, the “party convicted shall nevertheless be liable and subject to indictment, trial, judgment and punishment.”

The word “convicted” is key, because Mr. Trump was never convicted in the Senate. Rather, he was acquitted, with the 56 senators voting to convict falling far short of the two-thirds needed. Nearly half — 44 — of the senators voted to acquit Mr. Trump of the insurrection charge. 

Not everyone agrees whether the acquittal enables a defense on double jeopardy grounds. It’s a possibility, though, to which the House GOP seems oblivious. The conference chairwoman, Representative Elise Stefanik, and Representative Marjorie Taylor Greene are pushing the effort, designed to make it as if the impeachment “had never passed the full House of Representatives.”

“We are going to expunge the impeachments of President Trump,” Ms. Greene said at an event last week. “I’m very glad to let you know that the speaker of the House, Kevin McCarthy, came out in support just yesterday.”

“I think it is appropriate,” Mr. McCarthy said of the effort. “Just as I thought before — that you should expunge it, because it never should have gone through.”

“The American people know Democrats weaponized the power of impeachment against President Donald Trump to advance their own extreme political agenda,” Ms. Stefanik said in a statement.

Like most major issues up for a vote in the House, the issue appears on track to divide the conference, with members on the party’s right, like Ms. Stefanik and Ms. Greene, pushing the measure and members in vulnerable districts hesitant to endorse it.

Other members, like Congressmen Dan Newhouse and David Valadao, the only remaining House Republicans of the 10 who voted to impeach Mr. Trump in 2021, would likely be expected to vote against the measure.

Congressman Dan Goldman told CBS News that the effort is a “further continuation of the House Republicans acting as Donald Trump’s taxpayer-funded lawyers.”

“It is telling who is introducing them and it’s essentially whoever is trying to curry the most favor with Donald Trump,” Mr. Goldman said.

One Republican, Congressman Don Bacon, said he wasn’t in favor of expungement at the moment, telling CNN that “It sounds a little bit weird to me.”

Ms. Stefanik and Ms. Greene have also introduced a resolution to expunge the first impeachment of Mr. Trump from 2019, though this has not drawn nearly as much attention. 

Both of the expungements are resolutions, which means that their purpose is to express the sentiment of the House and are not legally binding. So even if passed in both the House and the Senate, they would not actually have an impact on Mr. Trump’s legal standing. The resolutions are also not likely to be taken up by the Democratic Senate.

Still, the prospect of a potential expungement in the House raises the question of whether the constitutional protection against “double jeopardy” — being charged twice for the same crime — would apply to Mr. Trump because of the overlap between his second impeachment and any charges related to January 6.

This question has been addressed by legal scholars and federal officials a few times in the past but never resolved. In 1973, the solicitor general, Robert Bork — a future federal judge — argued that impeachment-related votes could be “influenced by political passions” and senators could also vote against conviction on impeachment even if they understand an offense to be “punishable in the courts.”

The issue came up again in 2000, during the impeachment of President Clinton. One of Mr. Clinton’s attorneys, Nicole Seligman, arguing for the dismissal of the case, told the Senate that “the criminal law will still have jurisdiction over Bill Clinton the day he leaves office.”

An official in Mr. Clinton’s Department of Justice, Randolph Moss, however, conceded that there was “a reasonable argument” that the Constitution “should be read to bar prosecutions following acquittal by the Senate.”

Neither Ms. Stefanik nor Ms. Greene’s office immediately responded to a request for comment.