Removing purchased ringtones from iPhone
Backing up and restoring your iPhone would restore the ringtones again, and thus is a pointless exercise.

Connect your iPhone to a Mac/PC with iTunes installed. Select you iPhone in the toolbar, locate your iPhone under Devices in the sidebar and click on Tones. You'll should be able to locate the purchased and custom ringtones.



Select the desired ringtones to remove, right click and select Delete from Library option in the context menu.



You'll be prompted to confirm your action. Click on Delete button to complete deleting downloaded and custom ringtones that were installed on you iPhone.