For starters, a mailed offer and customer agreement should mention the actual name and address of the chartered depository institution taking the deposits. Then, you or a friend or family member willing to do a little extra research can then go to the Federal Deposit Insurance Corp. Web site and search for the institution's call report or thrift financial report, by clicking here.
Follow that link and, for report type, select "Call/TFR." Then type the institution's name to search for it. If no report comes up, and we are in the middle of the quarterly cycle when banks file their financial information with regulators, you may need to go back a quarter when selecting the report date.
The call report includes the bank's address right at the top.
The credit card offer should also include a customer service phone number. Call them and speak with a representative, to make sure you know which bank is involved. If they don't provide a customer service phone number, they are already making things difficult. Take your business elsewhere.