Okay, so I got it right, she would give her a necklace. We are starting to get to know more about the character's past and what has shaped them to be the people they are today, but it seems we are going to see a dramatic turn soon, as the gift purpose was kind of "misinterpreted", Nan Zhi did say she wanted their relationship to end, that's why she wanted to give a gift, as to get even, but she didn't mean to make it about the ship.