Byzantine Catholics are Catholics in full communion with Rome. St. Mary Magdalene Church is part of the Eparchy (diocese) of Parma, itself part of the Archeparchy (archdiocese) of Pittsburgh. The Archeparchy and its three eparchies, make up the Byzantine Catholic Metropolitan Church sui iuris in the United States.
“Sui iuris” is a canon law term meaning “self-governing.” (There are, in fact, 22 sui iuris Eastern Catholic Churches within the larger Catholic communion centered in Rome – 14 of them in the Byzantine tradition. All are in full communion with the Holy Father, the Pope of Rome.)