Is it permissible to work for an information technology company contracted by a bank, such that the contract is with the company and the salary is from it, but the work serves the bank?

There is no objection to providing services to Islamic banks. As for usurious banks, it is permissible to work in companies that deal with them if direct involvement with usury can be avoided. However, if the work necessitates direct assistance to usurious banks, then it is not permissible to remain in it, due to the Almighty's saying: "And do not cooperate in sin and aggression." And the Messenger of Allah, peace and blessings be upon him, cursed the one who consumes usury, the one who feeds it, its scribe, and its two witnesses, for it entails the prohibition of assisting in falsehood.