My iPhone 6 is brand new. When setting up favorites I somehow tagged my sister as Facetime instead of "audio." How do I remove the Facetime designation? I tried to edit it in Contacts but that category was not available.
You can edit her contact on your Mac and remove FaceTime that way. As long as you're using iCloud drive and have your settings setup correctly on your Mac, you can sync your contacts and edits from there. That's how I do mine and the changes appear almost immediately on my iPhone and iPad.
If you mean that you added her FaceTime credentials to the Favourites tab in the phone app, then just delete that favourite and re-add her. When you add her again, be sure to select the phone option in her contact details.