Does the Catholic Church recognise the Greek Orthodox Church as part of itself?

No. As a matter of fact there is no one Greek Orthodox Church. There are many independent Greek Churches. They originated by rebellion against the Catholic Church in the ninth century, and have split up into many different allegiances. As long as they refuse to submit to the authority of the Catholic Church they are as much outside the Catholic Church as the Protestant variations.

Radio Replies Volume 1 by Rev. Dr. Leslie Rumble MSC and Rev. Charles Mortimer Carty