There are various scenarios when it comes to accepting gifts from a bank:
If the gift is offered to someone who has no connection with the bank, such as one who is neither an employee nor an account holder; then it is permitted to accept the gift.
If the gift (in cash or other forms) is offered to an existing account holder or, as an incentive, to someone opening an account; then:
If it is agreed beforehand or expected due to customary practice, then it is considered an interest-based transaction and as such unlawful. As such, in accepting gifts from the bank, one derives benefit from the loan forwarded, and hence the gift is a form of unlawful interest (riba).
If there is no prior agreement between the depositor/account holder and the bank, neither is it customary for the bank to offer gifts to its depositors; rather, if the bank on its own accord offers some cash or gift, then it is permitted to accept it. In this case, the gift will not be deemed as interest.