You might need to contact tech support of visit your local Apple store if you have one in your area
If you cannot access settings, I would question what is installed to the phone. If you're not running iOS 9.1, get it installed for the sake of security. iTunes can help with that.
If you can access the settings, go to Settings > App Store and make sure you are signed into the App Store. Apple does not require a credit card to be present on the account for purchases/'purchases" if you already have an account, so you should be able to remove any card at the next "Enter card payment" prompt or just select "None." The only time a card is mandatory is if you have subscriptions like iCloud storage or magazines on your Apple ID.