Well, if the Avengers meet Peter's girlfriend, it depends on their own personalities and what they've heard about her. If they've heard good things from Peter, some like Spider - Man himself would be very excited to introduce her. The Avengers might be a bit cautious too, because they don't want any harm to come to Peter or their team because of her. For example, if she has a past that's a bit murky, they'll be on high alert. But if she's just a normal, nice girl, most of them would eventually warm up to her, except maybe those who are more cynical like Loki (if he was somehow part of the Avengers in this fanfiction), who would always be suspicious.