This reply was a little confusing to understand, but when you click the edit notification does it take you to the thread or a specific post?
incapaz already clearly outlined this, but to reiterate: you only get edit markers on someone else’s post if you flagged them and they edited the post to remove the flag. If the edit markers are for your own threads then they were modified by TL3+/staff; if it was a post then it was by TL4/staff. Those markers typically don’t show up for any other reason.
This doesn’t seem like a bug; or maybe it is, but it certainly isn’t major. For reference, could you check the post which the edit notification is redirecting you to for a “You flagged this” message near the bottom? You could also screenshot the post but blur out the username and icon (and the text body as well), it’s more important to see the messages appearing near post controls.