This division shall not be applicable to any transaction relating to a bank credit card plan. “Bank credit card plan” means a credit card plan in which the issuers of credit cards, as defined in subdivision (a) of Section 1747.02 of the Civil Code are only: banks regulated by or under the supervision of the Federal Reserve Board, the Federal Deposit Insurance Corporation, the Comptroller of the Currency of the United States, or the Commissioner of Financial Institutions of this state under Division 1 (commencing with Section 99) of the Financial Code; or, persons controlling these banks, provided that the assets of such a bank or banks represent a majority of the assets on a consolidated basis of any holding company system of which the card issuers may be a party; or, persons controlled by these banks.