The FBI should've conducted the investigation.
They should've questioned the justices along with everybody else, and in fact more thoroughly than anyone else.
They should have questioned Clarence Thomas in particular about discussing court matters with his wife, as staffers were questioned about discussing these matters with their spouses.
They should've questioned Samuel Alito in particular about the allegation that he has leaked information about at least one ongoing case before, FFS. (Hobby Lobby, 2014, alleged by Rev. Rob Schenck)
Depending on the results of an FBI investigation, consequences including criminal charges and of course impeachment should've been considered.
In my view, Thomas should already be facing impeachment given his wife's deposition before the Jan. 6 committee, and she should also be investigated by the FBI for her role in the insurrection.
This is how you restore the integrity of the Supreme Court-- by holding its justices accountable per Article 3 of the Constitution.
What can "the Judges, both of the supreme and inferior Courts, shall hold their Offices during good Behavior" even mean, if Thomas and Alito are assumed, in spite of all evidence, to be practicing "good behavior"?