how do i remove the payment method on iOS 10.3.3?

Assuming that you did have sucess getting into the area that I described, the suggestions in here might help. Not everybody can select None as a payment option, but take a look here.

If you can't choose None when you edit your Apple ID payment information - Apple Support

No, you aren't reading or correctly. I made the same mistake myself. It states "if you want to remove your payment information".... and that applies to any iOS version that you are running. The section about using iOS 10.2 or earlier would apply to changing payment information - not removing it.

Give this a try. I tried it myself and I am running iOS 10.3.3.

If you want to remove your payment information, or if you're using iOS 10.2 or earlier:

1. Tap Settings > iTunes & App Store.
2. Tap your Apple ID, then tap View Apple ID. You might need to sign in.
3. Tap Payment Information.
4. Change or remove your information. To remove your payment method, select None. Get help if you don't see None or can't select it.
5. Tap Done.

If you change your payment method to a credit card, the iTunes Store places a temporary authorization hold on your credit card to verify your updated account information.

Without specifically explaining what you are doing, we don't know what to tell you. You can, however, look here for help.

Change or remove your Apple ID payment information - Apple Support