Based on this answer about what it takes to destroy a Horcrux, it seems that the key requirement is being damaged beyond magical repair (at least according to Hermione).
“Exactly,” said Hermione. “Our problem is that there are very few substances as destructive as basilisk venom, and they’re all dangerous to carry around with you. That’s a problem we’re going to have to solve, though, because ripping, smashing, or crushing a Horcrux won’t do the trick. You’ve got to put it beyond magical repair.”
Harry Potter and the Deathly Hallows, chapter 6: "The Ghoul in Pajamas"
"Beyond magical repair" is a bit of a fuzzy limit, generally taken to mean Nagini (and by extension Harry) needed to die to destroy the Horcrux associated with them.
However, George Weasley's ear creates an interesting possibility, as it's cut off by Snape's Sectumsempra, and is explicitly beyond magical repair:
'I think so, although there's no chance of replacing his ear, not when it's been cursed off -'
Harry Potter and the Deathly Hallows chapter 5: "Fallen Warrior"
Assuming a Dark Lord with a decidedly twisted sense of humor (and no common sense) snuck into the Burrow when George was a child and made that particular ear a Horcrux, it stands to reason that having the ear cursed off in that manner would put it beyond magical repair and destroy the Horcrux, leaving George both holey and Holy (at least in comparison).
Is there anything preventing the use of something like Sectumsempra to magic off the bit of Harry's forehead with the scar to get rid of the Horcrux?
A note on J.K. Rowling: due to her unfortunate tendency to contradict herself, "Word of God" evidence rates lower than Cursed Child, which rates lower than Pottermore, which rates lower than the books.
I'll happily accept any evidence presented, as long as it's not contradicting something more trustworthy.