There is no provision for such restoration in the US Constitution, and there is a specific provision for an impeachment and removal denying the removed person any future ability to hold office. Article I section 3 says (in relevant part):
The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two thirds of the Members present.
Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law.
Note that impeachment is an exception to the presidential pardon power. Thus a President explicitly cannot undo a past impeachment and removal.
Impeachment and removal seems to have been thought of as a special kind of crime, with the Senate acting as a Court. (The exception to the pardon power supports this. If it were thought of as a recall from office, a pardon would not be applicable.) If so the disqualification would be considered part of the sentence. It is not usual to overturn criminal judgements by legislative act.
However, all that can be said for sure is that no Congress has ever passed a bill or resolution reversing a previous impeachment, so there has been no occasion form any court to rule on the effectiveness of such an action by Congress.