Letters can be ignored. Lawsuits must be responded to. And that same 35K will be offered as a deal after they file, if they file. They are trying to save THEIR legal costs, not yours. Let them sue. Fight it in court. Hopefully win. Counter-sue for your legal fees. Booyah.
Note: IANAL, and any actual lawyer would be less flippant. But seriously... don't let attorneys bully you.