First this happened to a client -- and now it has happened in a slightly different configuration to me. We have become victims of a classic protection scam.
You know -- the hire us to keep bad things from happen. But in this case the nuance is the bad things happened -- and it is pays us to stop the pain.
The slums of the internet are populated with so called "Consumer Protection" sites where some unverified anonymous person can come on and bash your company and your reputation. When you contact the company they flood you with a defiant list of legal precedent that shows they can keep it up.
Someone of the worse then blatantly say that they will take down posts that are proven false. When you ask them where you should send the proof they say -- oh it will cost $15,000 to launch the investigation. WTF?
Of course you can contact one of the companies on the website that claim they can protect your reputation. They either send legal letters to the company or they try to flood the internet with positive posts to bury the offending post. There are problems with both of these models.
Meanwhile I have a client that loses customers because of a re-printing of a irresponsible "news" paper article that slander them -- without posting the follow-up information
And I can't afford the price of either paying the tribute or for someones to bash their kneecaps. Meanwhile my kneecaps really hurt.
How do we shut these scum-buckets down? And what do you do to respond?
Are they located in the US? If so I'd try a small claims case, just to test the waters for free. Claim $5k in damages, the max for small claims. If you win, the door opens to new lawsuits by others and by yourself. If you lose...you're back to square one and forced to choose between eating it or hiring a hacker to delete their entire site.
I am tempted to say, "that's the price you pay for a wide open internet" but I wont. However, this really is an abuse of free speech. It goes much further than a single individual; how do you think Proctor and Gamble felt when their logo was likened to a satanic symbol and their sales and stock plummeted? The greatest strength of the internet is also it's greatest weakness. It empowers the tiniest of us to have significant impact on the giants around us. This, in no way, makes it OK for the kind of slander you are describing, but I do think there really is very little we can do about it, except maybe everyone should learn to follow that old adage to take things with a grain of salt.
To answer your question: 1. Build as many positive references as you can to surround the negative with multiple positives and 2. Counter-punch the negative with a "This publication is a scam" article, prominently placed on the offenders search results to counter act the effects when someone decides to research the errant claim. Good Luck!