I'd just call the person on the note. They might want to just pay the cost out of pocket for getting it fixed, because they don't want THIER rates to go up. Or they might want to put it through their insurance company. I'd give them the courtesy of a call first, since they were nice and honest enough to leave a note.

No, your rates won't go up. They only go up, potentially, if you file a claim and your insurance company has to pay. For example, if the people did not leave a note, and you got the van fixed under your own comprehensive policy.