I personally can't speak for the Catholics in Greece, but I do have one thing to clarify. Kephapaulos, you may already know this, but perhaps others here do not.
The term "Greek Catholic" is not typically used to speak of the Catholics in Greece specifically. The phrase is one of several used to identify the Catholic counterparts of the Eastern Orthodox Churches and faithful. The idea is that they (both the "Greek Catholics" and the Orthodox) practise their religion, using the same rites as received from Constantinople (Greece). Many people, particularly in the West, are more familiar with the terms "Eastern Catholic" or "Byzantine Catholic", but the use of the word 'Greek' is still perfectly acceptable. In fact, it is part of the formal title of the Ukrainian Church: the Ukrainian Greek Catholic Church (UGCC).