The credit card bank is responsible for obtaining a written authorization and for the contents of that authorization under Reg E §205.10 and for providing you with a copy of that authorization. It or your deposit-holding financial institution is responsible for complying with the notice of transfers in varying amounts requirements of §205.10(d). Typically, it would be the credit card bank that does it because it's in the best position to do so.
Your deposit-holding institution would be the one you'd go to if there were an error in one of the transfers, though.
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John S. Burnett
BankersOnline.com
Fighting for Compliance since 1976
Bankers' Threads User #8