What you do now is get a lawyer.
Do not say one more word on the subject. Not in writing, not in public, not even to your friends over beers, until you get a lawyer. Think of it like the Miranda rule -- now that a legal dispute has arisen, anything you say can and will be used by them against you.
What you shouldn't do now is panic. They've sent you a letter demanding a large sum of money? Big deal, anyone can send a letter. It's not unusual for people to try to bully others by having their lawyer draft a letter full of scary-sounding language that, when parsed by a lawyer, actually says nothing. These people hope you will read the letter, panic, and do something stupid like trying to settle with them before talking to a lawyer.
Don't give them what they want. Get a lawyer.