No way to 'Delete or Remove' my payment method

Is it possible to remove a payment method from Itunes and if so how? Must I have a valid payment method? On iphone, I'd like to remove my credit card info as the simplest way of preventing unauthorized purchases. I am unable to do this. I am unable to remove payment information from 'edit your account settings' page of 'Secure1.store.apple.com' - there is no option to remove the credit card, I can only edit or add a credit card. On the iphone, when I go to Settings / Itunes & App Store / Apple ID .... / View Apple ID / Payment Information - under 'Payment Type', 'NONE' is not an option that appears, and I have verified that I do not have a balance owed. On iphone, under Family Sharing which is shared with my wife, I see the credit card info, with no option to remove it.