The Parker family is, for lack of a better term, all seven flavours of messed up. Poor Petey is technically related to J. Jonah Jameson - who is both his boss and a raging collection of anger issues - and it's still unclear if his mother is actually his mother, or in fact his aunty.
This wild time is made a touch more wild by the fact that it's later revealed Peter has a secret sister. Not only was Teresa's birth kept a secret from even Peter, she was sent off to be adopted after their parents died, leaving Spidey with no way of uncovering his hidden sibling.
Or, at least, that was the case until she saved Peter's life, and revealed the small plot twist of who she was to him. Although Spider-Man is initially pretty surprised, he deals with it characteristically quickly. After all, in the grand scheme of his life, it's not even in the top ten weirdest things that happened to him that week.
Plus, she is a secret agent, and discovering your secret sister is also a secret agent has to be a double scoop of badass news.