It could be that she secretly likes the smell of it, which is a bit of a personal and intimate reason. In the context of the fanfic, it might also be a symbol of their relationship, and by stealing it, she's making a statement about how she feels towards him, whether she realizes it fully or not.
He could also playfully try to get it back, leading to a bit of a chase or a fun exchange between them. This would add some light - heartedness and interaction to the fanfic.
The plot could be that Percy discovers an old sweatshirt in his attic that turns out to be a magical artifact from one of the gods. Maybe it gives him the power to control water in a new and unique way, and he has to figure out how to use it without getting into trouble with the other gods.
Annabeth is known for her intelligence and strategic thinking. She is a strong and independent character. Percy, on the other hand, is brave and has a strong connection to the water due to his father being Poseidon. In the fanfic, when Annabeth sits in Percy's lap, it might be a way to show their unique relationship which has developed over the course of their many shared experiences in the Percy Jackson universe.
Percy might develop more of a steely determination. In Tartarus, he has to face extreme danger, which could make him even more resolute in protecting Annabeth and getting out. Annabeth, on the other hand, could become more resourceful. She'd have to use her wits in this strange and deadly place.
Annabeth might be initially speechless. She'd look at Percy with a mix of disbelief and love. After a moment, she would throw her arms around him and say 'yes' while laughing. She would then start thinking about all the adventures they could have as a married couple and how they could build a future together in both the mortal and demigod worlds.
She might initially be shocked. Annabeth is a strong character, so she could start by trying to stand up to Percy verbally, asking him why he's being so mean.
In this fanfic, Percy could develop a darker side. The horrors of Tartarus might make him more ruthless when it comes to protecting himself and Annabeth. Annabeth, on the other hand, may become more empathetic. She could see the pain and suffering of the other beings trapped in Tartarus and try to help them, which would shape her character in a new way. Also, their relationship would develop further. They would have to trust each other completely, and this could lead to a more mature and deep connection between them.
She could start by being honest with Percy about her feelings. Just come clean and say why she wants to get back together. For example, she might say she realized she can't live without him. This straightforward approach might help Percy see that she is sincere.
A fanfic could also depict their kiss in a more unexpected situation. For example, they get magically transported to a different realm. In this strange new place, they only have each other. The fear and the uncertainty of the situation bring them closer. And finally, when they find a way out, they celebrate by kissing. This kiss is a symbol of their bond and their ability to overcome any obstacle together.