Since both parents wrote conciliatory letters, it would seem some response is in order, otherwise it could be taken as rebuke on your part. Depending on their code of etiquette, no response could make the situation even worse.
To me the KISS principle is important here. Acknowledge their letters, thank them for breaking the ice and then play up the special occasion in their daughter's life. All on a positive note.
I read your post several times and did not see anything to indicate the parents' acknowledgement or awareness of their daughter's behavior which led to your breakup. It may be that either they do not know of it, or are unwilling to accept it and therefore blame you.