A Dodd-Frank Act provision requiring the president to provide a reason for firing the Consumer Financial Protection Bureau’s director may pass muster with a pair of federal appellate judges hearing a challenge to the bureau’s constitutionality.

Judges Patrick E. Higginbotham and Stephen A. Higginson of the U.S. Court of Appeals for the Fifth Circuit raised questions in March 12 oral arguments about just how much the for-cause firing provision—intended by Congress to insulate the CFPB from outside interference—actually limited the...