I think “deceive the integrity” means that the administration wouldn’t have been in the position in the first place to agree to anonymize the donation if not for Ito’s actions.
Except Ito wasn’t the only faculty member taking money from Epstein, and the Media lab wasn’t the only department. The thank-you letter to Epstein that Reif signed was for money Epstein gave to support Seth Lloyd — a professor in mechanical engineering and physics — and the earliest known money from Epstein after his conviction. The ‘if not for Ito’ reading doesn’t make sense.