The Joker's scars in an Earth-3 origin story turned him into a hero, inspired by humiliating Owlman. Owlman scars Jokester after being mocked, inadvertently creating a hero instead of a villain.
It's obvious that the Joker is a disturbed individual with a troubled past, and this is hinted at several times in the film when he attempts to tell an origin story about his facial scars.
Then, just out of focus in the background, we see him carve a smile into his face, an unmistakable nod to The Dark Knight's Joker's scars. Oh, brother. Why is Joker: Folie à Deux's reference to ...