Public IP Display sends blank, anonymized* HTTP GET requests to the external, 3rd party websites specified in its source code and user preferences, at the specified interval or when specified events occur, and to the specified destination URLs.
The author of this addon has no control over these 3rd party websites and will not accept responsibility for issues such as your HTTP GET requests and their inherent information (the user's IP address and other details) being logged or any other incidents involving these 3rd parties.
TL, DR: you use this add-on at your own risk.
Users are free to contact the author at the specified support email address or source code repo/bug tracker to request removal or addition of particular IP engine sites.
*Firefox internal feature provided by Mozilla and used as-is