How to remove payment information

The bottom line is that you can only change one payment method for another payment method or by choosing the None option from the accepted payment methods.

ASC - Late 2012 Mac mini, macOS 10.13.6;  Watch, 38 mm AL, watchOS 4.3.2; iPad Air 2 & iPhone 8+, iOS 11.4.1; TV 4th Gen, tvOS 10.4.1;  Airport Express

Change or remove your payment information from your iTunes Store account (Apple ID) - https://support.apple.com/HT201266 - "On your iPhone, iPad, or iPod touch, you can change the payment information for your Apple ID in Settings. On your Mac or PC, you can change your payment information from the iTunes Store." - More information at: https://discussions.apple.com/thread/3251676?answerId=15891166022#15891166022 and another tip at https://discussions.apple.com/thread/8010960?answerId=32902784022#32902784022

If you can‘t choose None when you edit your Apple ID payment information - https://support.apple.com/HT203905