Having others take down your picture will probably not have any legal action. This is a scam that, so far, is completely legal. Various private companies are either purchasing or otherwise gaining access to public records. These public records can include the record of your arrest and your booking photo. Then they post this information online. These private companies are not saying anything that isn’t true, for example, you did get arrested for the charge. Since they are not saying anything that is not untrue, you have no legal recourse.
Trying to remove the information is both expensive and not likely to work. In fact the websites themselves will charge you to take the information down. Often, this is a scam because your payment only gets your picture taken down from one site but not all of them. And there is nothing prohibiting them from putting your picture up on another site. Some of the sites will take your information down if your charges are dismissed and that is certainly worth doing as it won’t cost you any money.
There are some companies that will try to clean up your online reputation by posting positive information about you with the hope that the good stuff fills up the first few pages of Google so that there is no room for the bad stuff. This might work, but it is very expensive.
Sealing or expunging your record won’t help either because the court order only applies to public records, not privately owned copies of public records.
The unfortunate result is that there is very little you can do. Private companies are able to post public records of your arrest and booking photo and it is hard to fix this problem. There isn’t anything you can do that will be cheap and guaranteed to work.