The Avengers meeting Peter's girlfriend could also bring out a protective side in Peter. He might be worried that they'll be too hard on her or that she'll be in danger just by being associated with them. Meanwhile, his girlfriend could be trying to fit in and prove that she's worthy of being around such powerful heroes. It could also be a situation where she has to deal with the jealousy of some of the Avengers' female members, if there are any. Or she could form a special bond with one of the Avengers, like Natasha Romanoff, who could become a mentor - like figure to her.