Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Working for banks
According to the rulings of eminent scholars, one may work in banks in areas where you are not directly dealing with interest.
However, if you find another job that is wholly free of taints of interest or haram, you should go for it.
Otherwise, you may continue. However, according to the rules of jurisprudence, we are excused of matters that we have no control over. That is known as `umum al-balwa or unavoidable necessity.
Having said this, I would also advise you to continue to purify your income by giving optional charities that you can afford to and making lots of istighfar (seeking Allah’s forgiveness).
Almighty Allah knows best.