Katara doesn't wear any necklace even after Aang created a new one. In episode #1.14 "The Fortuneteller", Aang creates a new necklace for Katara with Sokka's fishing line after Katara lost her mother's necklace and that Zuko found on the prison floor in episode #1.6 "Imprisoned". During the rest of the episode #1.14 Katara doesn't wear any necklace, and only wears a necklace again at the end of episode #1.15 after Aang recovers her lost necklace from a duel with Zuko in the monastery.