Praise be to Allaah.
There is nothing wrong with using a covered or prepaid credit card, and there is nothing wrong with the company that issues it charging a fee for it that is higher than the actual cost, because this is a fee in return for offering this service. Rather, what is not allowed is charging more than the actual costs incurred in the case of an non-covered credit card, whether the additional amount is added to the fee for issuing it or to the transaction fee, because when the bank gives money to a customer when the credit card is not covered, this is actually a loan to him, and it is not permissible for the bank to charge interest or make a profit on this loan; it should be limited only to charging the actual costs involved in issuing it.
The basic principle is that it is not permissible to deposit money in riba-based banks, even if it is a deposit into a current account, because the bank uses the money to help it to carry out its transactions, both those that are permissible and those that are haraam. This is the rule except in cases of necessity, where one has to do deposit money in the bank so as to protect it and other cases of need, when there is no Islamic bank. We have previously quoted the words of the scholars concerning that. Please see the answer to question no. 152339
Based on that, if there is no Islamic bank that offers credit cards and you need to use one, then it is permissible to open an account in the riba-based bank, but it should be limited to depositing enough to cover the credit card.
And Allah knows best.