All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is not permissible to open a savings account in a bank that deals with Riba (usury) as this is a form of consuming Riba. It is known to all Muslims that consuming Riba is one of the grave major sins. For more benefit, kindly refer to Fatwa 84007.
As regards the gifts that a Riba-based bank gives to its customers, then it appears that it is not permissible to accept them for several reasons, among which is that the person who deposits his money in the bank is a creditor [providing a loan to the bank] and it is not permissible for a creditor to take a benefit from the debtor in return for the loan. Also, the bank gives such gifts to encourage the people to save money in it and to deal with it, and this is not permissible.
Therefore, anyone who took anything from those gifts is obligated to get rid of it by spending it in charitable fields. He is also obligated to withdraw his money from the bank that deals with Riba except in case of necessity.
Allaah Knows best.