If they're auto-charging it, don't tip any extra on top. Check every receipt because in many places you'll see they automatically add gratuity. This place is definitely shady for adding it as a "service fee" and then still putting suggested tip amount afterwards. I would say do not feel guilty and do not think twice. Service fee implies that it paid for the service.
This is the exact story that came to mind when I read the post. This one stuck with me for sure.