You can issue a credit to a credit card if you supply a transaction ID, amount, and last four digits of the credit card number. You can - I think - do the same thing with the last four digits of the bank account. There may be a time limit of 90 days on that, however. You can also issue something called an unlinked credit, which allows you to credit without a prior transaction - this doesn't come standard with your Authorize.net account and has to be requested via an application form. I would assume it also requires the full bank account number.
