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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
It is required that you put your money in a permissible account that does not deal in forbidden matters, and not in an account that deals in forbidden matters, even if the bank does not pay interest, because just to deposit money in it consists in helping it in what is forbidden, and there is no considerable necessity by which it would be lawful to deal with it as long as a permissible alternative exists.
The fact that those banks did not apologize for previous mistakes is not an impediment for dealing with it.
Dr. Hosaam Affaanah said in his book Yas'aloonak: “In principle, it is forbidden to deal with a Riba-based bank because most of its transactions are related to lending and borrowing money with interest and usury, which is absolutely forbidden; but because of the circumstances in which we live, in terms of the risk of keeping cash and the lack of Islamic banks, and in terms of trade and industry being dependent on dealing with Riba-based banks, then it is permissible to open current accounts in Riba-based banks, provided that one does not connect them with Riba (interests and usury). In case there is an Islamic bank in the area of the client, then it is obligatory to deal with this bank only, and it is forbidden to deal with Riba-based banks.”
Allaah Knows best.