At one point, Mr. Lauro said that Justice Thomas had “directed” Mr. Trump’s legal team to pursue the motion. But he quickly amended himself, saying only that the justice had raised the issue in his concurrence.

Still, Judge Chutkan interrupted him before he made his correction, asking archly, “He directed you to do that?”

And sitting silently in the courtroom watching the proceedings, Mr. Smith seemed to share the judge’s reaction, nodding emphatically.