To remove the card's details from your iTunes account, tap on your id in Settings > iTunes & App Store and then tap on 'View Apple ID' on the popup and log into your account - on your account's page there should be a payments link. Or you can do it via your computer's iTunes : go into the Store > View Account menu option and log into your account, and on your account's details click on the payment details link.
Changing payment info : Change or remove your payment information from your iTunes Store account (Apple ID) - Apple Support
If you don't get the 'none' option on the payment details screen : Why can’t I select None when I edit my Apple ID payment information? - Apple Support
What happens when you try to buy something ? If you are trying to gift content then you will need to have a credit card on your account, your balance can't be used for gifting ; if you are trying to buy for yourself and you have a credit card on your account then its details need to be correct and complete - but your balance should be charged for the purchase.