Eastern Orthodox Church is Catholic.
It is recognized by Rome.
The Eastern Orthodox Church does NOT need to be recognized by the Roman Catholic Church. They are SEPARATE CHURCHES.... completely.
I was assuming you used the words in their common sense. Personally, as a pious Orthodox Christian, I know perfectly well that the Orthodox Church is Catholic, in the sense of being the One Holy Catholic and Apostolic Church, spoken of in the Creed.
The adjective Orthodox only became a necessity when the separated Patriarchate of Rome kept loudly claiming the name "Catholic". If you follow the religion threads, you will notice that I scrupulously follow the patristic custom of refering to those in communion with the Pope of Rome as "Latins" and their communion as the Latin church--I will not rhetorically credit their claim to catholicity, even with the qualifying adjective "Roman". (Besides as the Turks and Arabs who conquerored the Empire knew and know, my spiritual forebearers along the shores of the Eastern Mediterranean were Romans, too, even if the old capital had been overrun and removed from the Empire, so the qualifying adjective wouldn't be much to the point.)