I've never had a credit card entered for my ID as I just use gift cards. But I would say if you go to settings - App Store and press on your Apple ID, then press View Apple ID, it will then load with a box, select payment information, this will load with another box with credit cards listed, I selected none here. See if you can select none here also and I'm thinking it will delete your credit card info, well I hope it does. Maybe someone who has done this will chime in here. If you want to then start using gift cards go to the app store under Top Charts and scroll to the bottom, press redeem and you can input the number for a gift card here.
Hope this helps you.
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