If the issue is it is ranking in the search engines, the goal should be to get the page deranked due to the falsehoods. Google et al will not do this unless it has received a judge's order or ruling about this. I'm not a lawyer, but what some people do is this: Write an affidavit of fact (put more simply, a notarized letter) itemizing the specific facts. Send it by mail certified return receipt to the party stating the falsehoods, and give them 21 days or so to reply. If/when they do not, they have (in UCC terms) "dishonored your presentments" and thus have defaulted on answering a challenge to their factual claims.
You might even do this 2 or 3 times to be sure, and have a third party (a lawyer, or the notary) be the one who the responses were to be sent to, and who can then state in writing they did not get a reply. Now you have enough of a paper trail of evidence to submit it to a local judge, so they can issue a "finding of fact" judgement on the matter, in your favor. Present this order to the search engine(s), and it should be enough to get that webpage deindexed/deranked. Check with your lawyer to confirm or perfect this method.