Is it permissible to benefit from money saved from working at an insurance company, knowing that it is deposited in an Islamic bank, and can a portion of the new salary be considered as repayment for the amount whose permissibility is doubtful?

If you were ignorant of the Shariah ruling concerning the first job, there is no blame upon you for using the salary after repenting and learning of its prohibition. This is based on the Almighty's saying: "So whoever receives an admonition from his Lord and desists, he may have what has passed, and his affair is left to Allah." It is more scrupulous to dispose of it through charitable means. However, if you were aware of its prohibition, then you must dispose of what remains of it, perform sincere repentance, seek forgiveness, and increase in righteous deeds.