...for the Feast of St. Andrew (patron of Constantinople), the Pope had restored the Patriarchate of Constantinople? By appointing a Catholic as Patriarch, that is what Pope Leo XIII did for the venerable Church of St. Mark in Alexandria: "We ... from the plenitude of apostolic power restore the Catholic Patriarchate of Alexandria and establish it for the Copts. ... To us it is most desired that the dissenting Copts look upon the Catholic Hierarchy in truth before God; that is to say the hierarchy which on account of communion with the Chair of Peter and his successors alone can legitimately restore the Church founded by St. Mark, and alone is heir of the entire memory, whatever has been faithfully handed on to the Alexandrian Patriarchate from those ancient forebears." (Acta Sanctae Sedis 28, p. 257-260, anno 1895-1896)
"The plenitude of apostolic power," said Pope Leo XIII: it would be temerarious to claim that the Bishop of Rome does not have the power to do what Leo XIII did at a moment when it appeared to him that many Copts would return to unity. No serious suggestion is being made here as to what Pope Benedict XVI should do for the feast of St. Andrew this year or next. But just as the Popes have varied greatly in their approach over the centuries to the schismatics of the East -- the Council of Florence treating the Patriarch of Constantinople and 60 Greek bishops as a legitimate deliberative voice with the Latins, even before the Greeks co-defined the Filioque with Pope Eugene IV, versus Leo XIII appointing a Catholic as Patriarch in the face of the schismatic Copt in Alexandria, versus Vatican II-era Popes and their well-known gestures and messages to objectively schismatic Patriarchs -- so also the Greeks have not been as monolithic over the centuries as sometimes supposed.
For example, John Bekkos, as a result of his study of "Latin" doctrine and the Holy Fathers, professed the truth of the Filioque and the Roman primacy, becoming Patriarch from 1275 to 1282 in full communion. The witness of his life would make it slanderous to accuse him of some sort of sellout for political reasons, and he professed the following in a document sent to the Bishop of Rome: “the due reverence of our obedience; the primacy of the Apostolic See; the highest and perfect primacy and principality over the whole Church catholic; the plenitude of power; to the same, all Churches are subject, and their prelates owe [to the Apostolic See] obedience and reverence." In addition, in line with Pope St. Gregory the Great, he professes that the Roman Church had confirmed and strengthened the privileges of other Churches. (PG 141: 945-950)
And even the Byzantine "hermeneutician of rupture" St. Symeon of Thessalonika could recognize the power, in principle, of the Pope, regardless of diatribes against alleged Latin heresies: "Let [the Latins] only show that the pope perseveres in the faith of Peter, that he is truly his successor under this aspect, and we acknowledge in him all the privileges of Peter, and we recognize him as the leader, as the head and supreme pontiff. ... Let the bishop of Rome only profess the faith of Sylvester, Agatho, Leo, Liberius, Martin and Gregory, and we will proclaim him truly apostolic and we will consider him the first of the pontiffs and we will obey him not only as Peter, but as if he were the Savior himself" (PG 155: 120-121; the original Greek is more accurately rendered in Dictionnaire de Theologie Catholique 14, p.2976-2984).