No matter how they call it, the Greek people and government have no problem with the affairs of the former royal family. Except for Constantine and Anne-Marie who are historically important since they were at some point diadoch/king and queen respectively, the rest of the former royal family of Greece are treated as regular celebrities. Rarely, if ever, anything is written about them in the official "legit" press. In contrast, pictures and news about them, along with singers, actors etc, appear constantly in Greek tabloids (the equivalent of the Enquirer) and glossy magazines like Hola.
Also, the "legit" press gives publicity to various events attended by the Queen of Spain and princess Irene, who are both extremely popular among the people.