First, I don't think LinkedIn would have any ground to stand on. Scrapping the public web, taking screenshots of public sites, posting those screenshots are not violations of copyright or trademark.

Secondly, censorship is almost always the wrong solution. I get wanting to promote peace, but you don't promote something by refusing/canceling any opposition to your idea. If your strategy to promote something is to silence any opposition then your idea probably sucks, and can't stand up to opposition.

Win on the battleground of ideas, not with the tyranny of forced opinion.

So you want LinkedIn to give this 3rd party website a cease and desist order? You could at best contact LinkedIn however I'm not sure they'll jump all over this.