The most likely situation is that the company who sent the letter hired a shady SEO. That SEO did spammy things that got them penalized. They brought in a new SEO to clean up the mess, and that SEO is trying to undo all the damage the previous one caused. They are trying to remove every link they can find since they didn't do the spamming in the first place and don't know which are causing the problem.

That IS a better theory that "I frequently get emails from random people on the internet who ask all sorts of insanely idiotic things", indeed.