How can I remove billing details in my iPhone and change it to none

On your phone tap on your id in Settings > iTunes & App Store and then tap on 'View Apple ID' on the popup and log into your account - that should give you a payments link on your account's page.

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