Bumped into another car recently - need advice

[MrZ]

The other night I was tired and was going head first into a gap between two cars (never do this - always reverse in!), and accidentally bumped into another car as I was doing so. The left rear side of my car hit the front bumper (right side) of theirs. I got out to have a look, and noticed not a huge amount of damage to my own car (almost all of it buffed out), but an unusually large amount of damage to the other car. The entire corner of the bumper looked like it had lots of existing damage from parking scrapes/scratches over the years. It was very hard to tell what was pre-existing damage and what was new. It was a fairly old car (20-year-old E46 BMW) and the other side of the bumper had no damage that I could see. Now I did the right thing and left a note on their window. They've since contacted me and are basically ignoring the fact that they very likely had existing damage on their bumper (I asked them this). I think they're just trying to get it fixed like new. Any advice on what to do here? Do I make them an offer of say, half of the quote they end up getting, or do I basically have to pay the full amount?