Is it permissible to pay the bank interest incurred on the remaining salary in the account for ATM card expenses issued by a non-Islamic bank?

If you are compelled to deal with an interest-based bank, there is no harm. However, you are not permitted to benefit from its interest earnings to pay off credit card expenses or other things, because these interest earnings are illicit money that its possessor is not allowed to benefit from, unless he is poor and in need. This money belongs to the general welfare of Muslims and is not his private property.