If it's indeed specifically about party invites and not other things, then you're right and I misread it. I wish the author were more explicit about that beyond

If it's indeed specifically about party invites and not other things, then you're right and I misread it. I wish the author were more explicit about that beyond just a fleeting line at the beginning "We ended up hanging out quite a bit during those early months." My read was that Anna never acted like she's actually part the group because she's only ever shown repeatedly declining invitations.