Is that correct?
Your understanding is correct. But, as explained below, the correctness of the prohibition is --at best-- highly doubtful.
The prohibition is pursuant to 18 USC 2265(d)(3), and it purportedly is premised on "such publication [being] likely to publicly reveal the identity or location of the party protected under such order".
The prohibition is futile because, in most cases, the respondent to that order already knows both identity and location (in addition to other information such as phone number, email address, workplace, and so forth) of the party who filed or was granted the request for protection order. Furthermore, in order to comply with the protection order, the respondent obviously has to know the identity of the person for whom the protection is granted and to whom the respondent is ordered not to approach anymore.
The prohibition as to disclosure of requester's location might be useful only in instances where the requester has relocated and is trying not to be traceable by the aggressor or stalker. But even there redacting the victim's location in those instances makes more sense than a prohibition across the board.
By contrast, many instances of domestic violence and harassment could be prevented if courts gave public access to these records. That is because a cautious person could do a search on an individual to ascertain whether associating with the latter is safe. For instance, consider the scenario where a female is thinking of dating some male of whose past she does not know something she should know for her safety.
what recourse does one have to take them down?
A simple notice or perhaps an informal request to the court might suffice. If that fails, the person would have to file a motion in that matter. If the motion is ignored or denied, the matter can be escalated to an upper court in the form of a petition for writ of mandamus or its procedural equivalent.
Nevertheless, since the prohibition supposedly is aimed to protect the identity and location of the victim, it would be odd for the respondent to argue he is interested in protecting the identity and location of his former victim. Obviously a respondent's interest in enforcing the prohibition of disclosure is to avoid the embarrassment and loss of reputation resulting from the protection order(s) against him.