K.B.
See if you can find out who the tutor's fav author is and give them a couple of nice hard-bound books (but they might already own those). You could also buy an inspirational book about teaching a child or something (I bet your local bookstore or Barnes & Noble Associate would have some ideas ). You could also give the tutor a nice card/make sure your daughter writes her name on the card and enclose and a gift card to a bookstore...