When it comes to art plundered in Europe during World War II, Ronald S. Lauder, chairman of the Commission for Art Recovery, has been very much the face, and soul, of the restitution movement.

In June, he was center stage at a Senate hearing on a bill to ease the way for the return of art looted by the Nazis, testifying alongside the actress Helen Mirren, who last year starred in “Woman in Gold,” a film about a Jewish heir’s struggle to retrieve her family’s stolen possessions.

Away from the spotlight, though, Mr. Lauder has been criticized for more than a decade by other restitution advocates and scholars. They say his own practices in detailing the provenance of works within a Manhattan museum he co-founded, the nonprofit Neue Galerie, and his private collection have not been as transparent as they should be.

Now there are signs Mr. Lauder has heard the criticism. To elevate their research, he and his staff have hired additional experts, are overhauling the museum’s website to ensure that provenances are more detailed and soon plan to announce a surprising byproduct of their labors: One of the Neue Galerie’s major works has a clouded history and may be returned to people who say they are the rightful owners.