At the time when it happened C said he would "polish it out" and we never heard anything more, a quick look at his car didn't reveal any damage so I assumed it was dealt with, until the message came.
I've spoken to C and he's been paid and has arranged a "mate's rates" repair.
If I'd been asked at the outset I could've arranged the repair myself, and paid much less.
I think the "right" thing to do is use your insurance, that's what it's for. C drives like a muppet and shouldn't have been close enough to a just parked car to hit it in the first place.
This ^^ is what I had in my mind when I said B/B's parents should have been in on the agreement (but didn't actually say so!)
IMO, 15-year-old B is old enough to take responsibility for not opening car doors at daft times, and from what you said, she accepts this.
If you can find out how much
you could have got the repair done for, consider offering that as a good-will gesture. After all, that is all it would have cost you/your daughter if they had bothered to ask you about it, rather than coming to their own agreement and then just expecting you to agree to whatever they had decided should be spent. Ask to see a photo of the original damage/detailed invoice, too - especially if the initial damage was so minor they were talking about polishing it out.
Edit: this is what NorthernDave has already recommended - I should read the whole thread before replying!