"si" / "sin" / "sitt" are used to describe that something (or someone) belongs specifically to that person and nobody else.
"Hun er kona si" means that "She is the spouse of that person." "Det er bilen sin" means that "That is the car owned by that person." "Han elsker huset sitt" means that "He loves his own house."
In the specific case here: "Hennes" could mean that you are drinking the tea she made for you. Or that you used her supply of tea to make yourself one.
Using "sin" here could work in a context, that you - for instance - drink ("steal") the tea she made for herself. "Jeg drikker teen sin" would mean that "I drink the tea that actually belongs to her and not to me."