The director of the BBC Trust said he was not "closely involved" in the preparation of a note on about the Byford payment.
Nicholas Kroll, conceded the payoff was "unquestionably a large figure" but a matter for the remuneration committee and not the trust.
In response, Jackie Doyle-Price MP told him the protection of licence-fee payer's money was "a matter for the trust".
Ms Hodge told Mr Kroll that the "the job of the trust is to protect the licence fee payers' interests".
She added: "There is not one person around the table who can understand why there was no challenge from you".