Is the cashback amount that the bank deposited into my account, which is designated for female customers’ foreign currency purchases, mine or the customers’, and how should I dispose of it?

What you are doing by mediating the purchase of goods for a fee is an agency for hire, and this is permissible if the goods are lawful and the fee is known. It is not permissible to mediate the purchase of forbidden items.

If the bank returns a portion of the customers' money or waives fees, these funds belong to the customers because you are their agent. You must inform them of this, and you are not permitted to take these funds except with their consent.

If you have a current account in the bank or a prepaid Visa card, and the bank gives you a gift, you are obligated to dispose of it by spending it on general Muslim welfare or giving it to the poor and needy. This is because a current account is considered a loan, and gifts on a loan are forbidden.