This AU is already wonderful but... What if Zuko thought he was the one who burned Katara's hands?
He notices her scars for the first time during his search for the Avatar, a few weeks after she got them. But he doesn't pay any attention to Katara during the fight, not really. It isn't until the Siege of the North that he truly sees the scars on her hands, and realises that they weren't there before (her hands had been soft and unblemished during the pirates incident, not like this, rough and darker and achingly familiar).
When did this happen? Was it during one of their battles? Was one of his men responsible? Or did somebody else do it? There is no doubt in his mind that these are bending scars, after all.
Zuko wonders, after the North, if he gave them to her.
He has always been careful with his bending, regardless of the rage and desperation that fuel his battles with the Avatar. He knows what being burned and forced to carry a constant reminder of the flames is like—he's incapable of causing such pain to anyone, not even an enemy.
But what if he already has?
It's a sickening thought, and it chases him during his travels through the Earth Kingdom, adding weight to his guilt. He tries to hold on to the thought that maybe, just maybe, somebody else burned the waterbender, and he isn't to blame. But time passes and he witnesses and does many terrible, beautiful things...
So he decides to carry the responsibility for the burns on the waterbender's hands. It doesn't matter anymore if it wasn't him who burned her—he might as well have.
When they meet again under the Crystal Catacombs of Ba Sing Se, he listens. She blames him for everything that is wrong in her life, and he accepts her rage, because he knows he can't defend himself against her. He doesn't want to.
He can be the face of the enemy. He's already a monster, after all.
But then she offers to heal him.
Doesn't she know he could be the one who burned her? Doesn't she care for all the stupid, horrible things he has done to her and her kin? Doesn't she see the ruthlessness and hate coursing through his blood?
But then she's touching his scar with her burned hands and she's reaching for the blessed water and he can't do this.
"Why? Don't you want to be free of your scar?"
"Use the water to heal yourself. I deserve to carry the weight of my sins, but you don't have to."
There's silence, and Zuko tries to tear himself apart from her touch, to get away from her and from the Catacombs and from the world. But her scarred, beautiful self reaches out for him again. Katara holds his face with her burned hands and gently forces him to look at her.
Flesh on flesh, scar on scar, they meet.
And somehow he knows what she's going to say next.
"Zuko, you didn't do this."