How do I get the credit card and payment stuff off my phone?

Before you can buy, change or remove you card details or payment methods on iTunes / App Store

You need to check what the outstanding bill on App Store purchases and outstanding balance by doing the following:

1. Open the “Settings” in iOS, then go to ‘iTunes & App Store’ and then select your Apple ID
2. Choose “View Apple ID” to access the Account Settings page
3. 
4. In the Account Settings section, go to “Purchase History” and scroll through the list to find any item with an outstanding balance – this is what must be paid before you can change your payment information
5. Once the balance payable is zero. Give it 2-3 working days.

Update your payment information as detailed below to stop the “Verification Required” error message on the iPhone or iPad

1. In the Account Settings section, tap on “Payment Information”
2. Under ‘Payment Method’, choose “None”
3. If you can't choose none or none does not exist. the reason could
   1. 1. App store for the first time
      2. Active Subscription renews automatically
      3. You are part of Family Sharing
      4. You are not in the country or region you’re creating an Apple ID for
4. 
5. Alternative change payment method
6. 
7. Tap on “Done” when finished adjusting your settings
8. Exit Settings, and return to the App Store of iOS where you are now able to freely download, install, and update apps without seeing any “Verification Required” message.

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

1. If you have an unpaid balance or payment due
2. If you have a subscription that automatically renews
3. If you're using the iTunes Store or App Store for the first time
4. If you are not in the country or region you’re creating an Apple ID for
5. If you changed your country or region
6. If you're a part of Family Sharing

Change or remove your Apple ID payment information - Apple Support

https://support.apple.com/en-us/HT201266