The Supreme Court justice Clarence Thomas dissented on Monday, showing that he would have stopped the enforcement of the subpoena issued by the House.
The committee is looking for Ward's records related to her role in the attempt to steal the 2020 election.
The committee is investigating the plot to overturn the 2020 election in which Thomas' wife played a role.
Thomas was the only justice who dissented from the court's refusal to block the release of White House records. In March, it was revealed that his wife had been in contact with White House officials about Trump's actions.
The justice's wife was enraptured by baseless conspiracy theories about election fraud and involved in a plot with the White House to overturn Trump's loss, according to text messages.
Email messages from Thomas to state lawmakers, including those in Arizona, revealed her efforts to pressure Republican state legislatures to reject Biden electors. The fake GOP slates, which included Ward, could be submitted to Congress as part of Trump's plan to get Mike Pence to reject Biden's electors and declare Trump the winner.
The high court was asked to block the lower court decisions. The case was declared one of the most important First Amendment cases in history and she said forcing her to comply could put a chill on public participation.
The way for the House panel to get Ward's phone records was cleared by the court. Justice Samuel Alito was one of two justices who dissented on the denial of Ward's request.
Thomas does not want to be involved in cases involving his wife's political activities.
The committee heard testimony from Thomas in September. She told the panel that she still thinks the election was stolen.
Justice Thomas ruled in favor of blocking the disclosure of Trump White House documents before his wife's text messages were made public. Congressional Democrats have called on him to resign or be impeached because he inserted himself into cases that appeared to defend his wife's political activities.
The need for the court to abide by a binding ethics code was highlighted by the continued participation of Thomas.