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.
The contents of this answer should be considered friendly advice, not legal advice (I'm a pretty friendly guy), and the answer should not be construed to constitute an attorney-client relationship. If you'd like actual legal advice, call me for a free consultation at 813-635-0222. Also, if you liked this answer as much as my big ego thinks you did, be sure to click the thumbs-up button!
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.
You are not my client. I am not your attorney. The above comments are not confidential, not "legal advice", and not "legal opinion". I am licensed as a patent attorney and in the State of Connecticut. Retain and consult an appropriately licensed attorney to identify the laws and facts material to your concerns.
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.
This is not legal advice but only general information. No attorney-client relationship is created without a written and signed retainer. I do not know all the facts of your specific situation, which will affect this general post. You can get more information at my websites: http://kindsvater.com http://internetmarketinglawcenter.com