Clay's mom is a lawyer, the lawyer for the defendant school. Clay is a potential witness. In fact he's a key witness for the plaintiff as he's talked about in the tapes; he's listed in the tapes; he knew about the poem, which was distributed in the English class; he talked to the guidance counselor and gave him the tapes; and he played a role in Hannah's suicide or so she says. There's no way on Earth Clay's mom could continue to represent the school. If she did, this would give the plaintiff's lawyer all kinds of grounds for appeal were this to go to trial.
I read the book too, but there is nothing about a legal case in it. It was added to the show, and I think it took away from the show. But it was put in because people wanted to believe Bryce would somehow be held accountable. He likely wouldn't have criminally, but he may have been civilly. I'm still not sure he would have, though.