The are a private business, albeit with a disgusting business model. You can search out many answers here on AVVO related to them. You can ask them to take down, pay them to take down, or ask an attorney to state the facts as you have above and write them a take-down request. If what they have posted is false, your attorney can advise to as to possible actions.
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There are very few guidlines in this scenario. Free and public means free and public. Arrest records of public records and anyone can look them up, mugshots is just making it easy for the public to earn money. Otherwise, follow Barry's advice.
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