@tyrerunner I have not found a solution. When I interviewed SEO specialists on my podcast, I asked them and they said Google would ignore them and not to worry - Which I can see when I look at the backlinks Google Search Console has.
The problem is all these SEO tools showing thousands of these backlinks and making it harder for me to use the tool efficiently.
I followed the backlinks and found I'm in good company in these lists of links, it's just too bad that the anchor text is wrong because some of those back links have a decent ranking.
I did go to some of the higher ranked sites and when appropriate, created my own content with links using the right anchor text in the hopes that the matching keywords would help make it clearer - but they have yet to show up on any of the SEO tools or Google.
I did have a few visits from Google looking for that service but I think they were from before I deleted the posts - so the keywords were there to match - I've since fixed that problem.
I deleted the posts on my site but the url doesn't disappear and the page it lands on was empty so I 301 the pages to a 404 telling visitors the site is about brand storytelling and linked to the different pages if they were interested. This 404 page was already developed for those times a page load messed up.
I asked Google - no one has answered me there.
I have offered to sell an ad page on my site to a company and 301 all the links to it. - Not sure if this is a good idea - but I'd like to benefit somehow
If you come up with a solution or a better way to deal with all this spam and still get good data out of Moz etc... please let me know.