Sorry to be answering so long after your post; hope you don't mind.

I think people (other than small children) who ask about ANY kind of scar on someone else have earned whatever they get (except physical violence). It is NOBODY's business about any scar anywhere on one's body, except for the owner of the scar. IMO.

Or, for that matter, any kind of mark at all--birthmarks, dark spots/liver spots, burn marks, etc.--on one's person is completely private (even though other's can see it). We can SEE all sorts of things on other people that we KNOW it would be totally inappropriate to ask about or comment on. At least I think most folks would know--obviously some don't!

Anyhow, I would like to suggest two options: one is to shut them down and the other is to bore them to death.

Shutting them down:
Repeat "I beg your pardon?" over and over again until they stop asking.
Or, nicely thank them for their concern, without answering the question.
Tell them nicely that you're fine now, and don't answer.
Saying "I don't discuss this." is fine, IMO.
Saying, "It's a private matter" is fine, or "It's none of your business."
Or, you can look all around you, then say "Oh, were you talking to ME?" and, of course, don't answer the question.
It is more effective, IMO, if any brief comment you make is followed by silence and a direct look into their eyes.

Boring them to death:

Now, I think this can be fun! Because, they have violated your privacy (or are attempting to), you have certain inalienable rights to use whatever verbal feedback you choose IMO.

I recommend making up an EXTREMELY LONG story, that has nothing to do with scars, and is EXTREMELY BORING and hard to follow, throw in lots of names (my cousin's friend's mother, Kathleen) and tangents...

Brief example: Oh, and about that time I went to Minneapolis--silly me, I went there in the winter, if you can believe that! But the one really cool thing was this sweet bed and breakfast I stayed at with my sister's best friend's cousin, Marie. It was one of those places that was like going back 100 years ago...except it did have electricity and all that, of course. And, the room had the cutest curtains, sort of country meets New York. But, anyways, as I was saying earlier, at that time I was driving a Chevy Nova, and it was always overheating, and with traffic jams, I'd just sit there helplessly and watch the needle of the thermostat climb, and hope to high heaven that the radiator didn't explode or something. And the job I was working made it really difficult to get to a mechanic because the hours were so varied. I just didn't know what to do at all. Then one day my bosses' racquetball partner, Jennie, said she knew a mechanic who would come right to your office and work on your car, and I finally got it fixed. But, it was so scary there for a while. But, to get back to what I was saying earlier, I'd been following all the NCAA basketball games, and I really thought Louisville would win. Well, I really HOPED they would; Pitino is such a great coach and he used to be at Kentucky where Tubby Smith is now. The Elite 8 games were just breathtaking. Did you see them? Man, I was so happy that Texas Tech did so well! Bobby Knight has only been up there about 3 years, and he has (well first of all) calmed down a LOT, and just worked magic with the club there. And, at the same time all that was happening, we started having the most incredible storms here! Just out of the blue, there was a hail storm that at my house had GOLF BALL sized hail, and luckily I was in town where it was just marble sized, and I was driving home (I had traded in my Nova at that point, and had a little station wagon) and the hail started so I had to pull in to a drive-through window thingy at a nearby bank (this was like 10 pm), until the storm passed. Well, really just until the hail stopped. And, my dogs don't do all that well with big storms, so I was worried about them, too!

Part 2: extremely similar to part one above. Maybe even repeat a few things.

If you enjoy making up stories, you can write it out, and have a whole little series of tales that you just happily string together, and if the questioner tries to leave, just block their way and say, wait, I haven't gotten to the funny part yet. But, be sure not to have a funny part (unless you tell a funny story but do it so badly it makes no sense and then forget the punchline), because that would be more entertaining than boring. Also, if you can throw something in about when you had the flu, and were just SO sick--and get as graphic as you like about just how sick you were and what your symptoms were.

Yeeee Haw! I bet they'll never ask THAT question again! At least not to YOU!

Anyhow, I am not making light of the issue you bring up, because it is extremely intrusive for someone to do that, and hurts you. That is not OK, at all, IMO. I guess it'd be nice to see anybody in that situation get in the driver's seat and take the rude asker on any little journey that the askee chooses.

I hope I haven't been out of line or offensive or anything like that. I guess I'm just a little bent in some ways.

Good luck (and give 'em hell!),
Shar