Repeatedly restoring deleted phone number for a contact on iPhone

First, determine which account provider that contact is stored in:

1. Launch the Contacts app
2. Tap "< Lists" in the upper left
3. Tap an "All [account name]" section
4. Browse the list of contacts and see if the contact of interest is stored on that account
5. Repeat step (3) until you find which account it's stored under
6. Quit the Contacts app on the iPhone
7. Use a browser to login to the account where the contact is stored (e.g. iCloud, Google, Microsoft), and edit the contact to remove that number. If the number was under the account "iPhone", then Edit the contact directly in the Contacts app.
8. Launch the Contacts app on the iPhone and check that the phone number is gone from the contact