The Anna Grisdale Incident occurs at the height of Stargirl's brief popularity at the school. This incident doesn't destroy our girl, but it plants a seed of mistrust in Stargirl's motivations.
When Anna Grisdale's grandfather dies, Stargirl attends the funeral. She cries, growing visibly upset. But here's the thing: Stargirl never met the man. And she has certainly never met Anna. At first, Anna thinks that Stargirl somehow knew her grandfather, but this is not the case. Anna's mother grills Stargirl about why she is there, and then throws her out of their house for invading their private moment.
This is a perfect example of just how hard it is for people to understand Stargirl. Because she is more connected to the world and people around her than the average Joe, she interacts with others in strange, seemingly invasive ways. Sure, she doesn't know Anna's grandpa in a traditional way, but she does know him as one person of the human race knows another. She honestly mourns the loss of his humanity, and as for the crying, well that's probably because she feels the pain that everyone else at the funeral is feeling. Remember, Stargirl is more than just observant; she feels what she observes.
The Grisdales do not get this at all. They see her as an unwelcome intruder who for some unknown reason is using this man's death for her own secret purposes, and in this sense, they represent the suspicion that everyone in the town has for Stargirl. They are the Hillari Kimbles of greater Mica.