NEVER EVER EVER pay anything to anyone if they are making claims like this.
Simply respond with "Our legal team's process requires a filed Cease and Desist to be sent directly to them with specific references to infringements based on your claims. Once they have received this, the offending content will be immediately rectified."
Even if it's your personal website. Don't even fucking bother with these people and waste your time and money worrying about it, be sure this is the very first step in any legal action over public content. They can't just jump to suing you or demanding money.
Scammers will fuck right off.