Yes, but my question wasn't "What if you had an unavoidable scar from laser surgery", my question was "would you feel harmed if I burnt my initials into some not-normally visible part of your skin" for no other reason than to say that I was there?

Even minor scarring adds to the bodies burden in healing, so I think it's hard to definitively say that the laser inscribed initials did not cause any harm or increased risk at all. After all, these were not strong, healthy people -- they were sick enough to require liver surgery... and one of them had to have followup treatment which is when the initials were discovered.