elizzieblack
Aang didn't manage to get back Katara's necklace from Zuko. He hates it. He wanted Katara happy. He wanted Katara. But things don't look good for him in the romance department. Katara doesn't seem interested most of the time. Whenever Aang manages to have a mildly romantic moment with her, she comes back to mom friend attitude straight after. He doesn't lose hope though. As Sokka said, the key part to hold another person interested is to act like you don't care. Maybe that's what Katara is doing?
Zuko still has the necklace. He keeps it a secret from everybody, even uncle Iroh. He holds on to it whenever things go bad for him. He thinks about it nonstop, he's paranoid that someone might find it. Although he likes keeping the necklace to himself, he wants to return it to the rightful owner. When she stops hating him, maybe?
Meanwhile Katara sticks to not wearing any necklace. Although from time to time Aang tries to give her another one, she never accepts them. She doesn't like the reason why her little brother is constantly trying to give her a substitute for the necklace she lost.
Because from time to time, she still thinks about her old necklace and the person who is currenlty owning it.