Hi - my name is XXXXX XXXXX I'm an Intellectual Property litigation attorney. Thanks for your question. I'll be glad to assist you.
Treble damages (triple damages) are available under federal copyright
laws if there's proof of INTENTIONAL infringement, etc. These damages aren't a given, so the claimant offering to give this up isn't really giving up anything he/she/it is guaranteed.
If you believe that the claim is legitimate, then you may want to consider trying to settle with them for a nominal amount. One thing to keep in mind is that copyright litigation is VERY EXPENSIVE, and most claimants do not want to sue because of this issue (also, it's usually required that the copyright be registered with the US Copyright Office). Thus, it's not cheap to pursue.
Thus, if you can make a reasonable offer, you can likely settle with the claimant.
Also, if you're not convinced of the infringement, you may want to consult an attorney before responding.
I hope this answers your questions, but if you need something further, please let me know and I'll be glad to respond.