We've seen it before, SEO extortion emails and negative SEO threats. Bill Hartzer recently got one and asked Google what to do.
The advice given is similar to what Google said in the past - don't pay them - disavow them.
John Mueller from Google responded to Bill on Twitter saying "I'd disavow" those links.
@bhartzer @schachin @methode Sorry to hear about the hassle -- this comes up from time to time. I'd disavow (& maybe send me the list). https://t.co/T0GkkI4p5j
— John ☆.o(≧▽≦)o.☆ (@JohnMu) April 4, 2017
Sadly, this stuff has been going on for years and years. This is one of the reasons Google came out with the disavow file tool.
Forum discussion at Twitter.