It's not extortion. None of us civil rights advocates are particularly happy about these companies, but you aren't forced to pay them to have your name taken off their websites. And you name was legally placed there from a public record. If they aren't reporting the truth, you can sue them for slander.
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Not extortion. Possibly fraud, depending what they "promise" to do for you. For example, broadly offering to "remove your mugshot from the internet" is not a promise that can reasonably be fulfilled. At best the offeror could remove your mugshot from websites they control. Because they (presumably) do not own the copyrights in your mugshot, they cannot honestly guarantee that all copies of your mugshot will be removed from others' websites.
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There is no extortion, defamation, harassment, invasion of privacy - or any other category checked for the question.
This type of easily accessible information about prior legal issues is something the digital age enables that was more difficult to obtain years ago.
The best solution may be to hire a "SEO" specialist that can help get more positive websites with your name ranked higher, thus burying the negative web pages about you in the search rankings so they are not as easily found.
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Business privacy laws Intellectual property Copyrights Personal injury and defamation Personal injury and slander Criminal defense Business Criminal charges for cybercrimes Fraud Criminal charges for harassment Privacy law Internet law Civil rights Personal information Expectation of privacy