I'm not sure what other "anonymous websites" are you referring to, but PubPeer in particular is not something I would associate with a term like "swindler website". I would recommend everyone unfamiliar with PubPeer to take a look at their FAQ to judge for themselves whether their rules and procedures are rigorous enough for a legitimate post-publication discussion platform.
First and foremost, one of the key principles of PubPeer is that every comment needs to be factual and verifiable:
Q: What can my comment contain? Facts, logic and publicly verifiable information.
A: By far the most important rule for commenting is to base your statements on publicly verifiable information.
Allegations of misconduct are forbidden on PubPeer. They are anyway unnecessary. Your audience on the site is mostly composed of highly intelligent researchers and scientists. They are quite capable of drawing their own conclusions if the facts are clearly presented.
You should also avoid personal comments about authors and speculation about researcher actions and motives.
All comments on PubPeer are moderated to ensure they comply with the rules. You mention your work being "attacked", "disparaged" or "deconstructed in a dishonest manner"; does that mean the comments in question were in violation of these rules, or just that they perhaps exposed uncomfortable yet real weaknesses of the work?
Either way, the preferred course of action is to follow the FAQ again:
Q: My paper has been commented! What can I do?
A: PubPeer offers you a permanent right of reply. We encourage you to respond on the site. There are special facilities for indicating author responses. We believe that honest, careful and competent authors should provide “after sales service” for their publications, by clarifying any points that readers find unclear.
By engaging in the discussion, you can explain points of your work that were perhaps misunderstood by the commenter or inadequately supported by the data included directly in the paper.
Finally, note that whatever you publish would always get discussed both in public (at conferences or in journals) and in private (at various group and department meetings or Journal Clubs around the world). PubPeer just provides a convenient platform for such discussion that can work in the 21st century. The alternative of publishing thousands of articles like "Comment on Comment on Paper X" simply does not scale given current publication volumes.