So this is in Crooked House universe, set off a ways in the future. If you haven't read that story, Tarrlok survives the boat explosion with extensive burn scars and a missing right arm.
s/8627572/1/A-Crooked-House
The sound of their daughter crying had sent both of them running from the kitchen. They found her sitting in front of the fireplace cradling burnt hands and Korra was immediately sweeping her up into her arms and bending water from the skin on her belt to heal her. The burns weren't bad, and it was only a minute before she set Anyu down on the floor again. They both knelt to ask her what had happened, but when she looked down at the healed skin of her palms it set off another flood of tears. Tarrlok and Korra's eyes met over her head. What was going on? Finally, through the fits of sobbing they could just make out something about wanting scars like dad's.
He saw Korra's face go pale and quickly stood, picking Anyu up as he went, and left the room. From the corner of his eye he could see the girl looking from the scars on his face down to her unblemished hands and back to the scars, but he didn't speak to her until they'd reached her bedroom. He put her down on the bed and sat beside her for a moment, carefully considering his words.
"Anyu, why do you want burn scars?"
"I just wanted to be like you." Her voice was barely audible and she wouldn't meet his eyes.
He stretched his left arm out, shaking back the sleeve. Even years later the scars covering most of his body were still red and ugly. "It hurts, doesn't it?" She nodded. "I almost died when I was burned. It's not a good experience."
She looked up and burst out, "But they make fun of you! The other children talk about you, and I thought if I could be like you too, then- then-"
He pulled her into a hug before she began crying again. "Darling, you don't have to do that. Even though it's been years, your mother still wishes she could have done more to heal me. It would break her heart if she had to leave you with scars."
"Oh," she whispered, tears springing into her eyes again.
"It wouldn't make me happy either. Your mother and I don't want to see you in pain. That would hurt us as badly as it hurt you. We'd rather see you smiling and playing with two good hands, not recovering in a hospital bed. That's what I'd like best, even if the other children do talk about me."
She managed to give him a shaky smile, and wrapped both of her arms around his neck and kissed him before he left the room. He went back to find Korra sitting on the couch and staring down at the white-knuckled hands she had folded in her lap. She didn't look up as he sat beside her and put his arm around her shoulders. Finally, she buried her face in his chest and threw her arms around his waist as he murmured reassurances to her. It would be alright.
