A disclaimer is necessary: the Eastern Orthodox Churches do not have a set belief on this. This addresses what a number of Orthodox believe about Catholics.
There are Orthodox who claim we Catholics are in heresy: they refer to papal infallibility, the Filioque clause and the Immaculate Conception for example. Yet simultaneously they believe only an ecumenical council can dogmatically define something or label something heresy. This is significant.
The first seven ecumenical councils, which the Eastern Orthodox accept, never address papal infallibility, the Immaculate Conception or the Filioque clause as heretical. So if we must only believe that which is taught by an ecumenical council, then why believe that such Catholic doctrines are heretical? If we must only go by what the ecumenical councils say and such councils never deem such doctrines heretical, then it must be safe to believe in these doctrines.
As mentioned earlier, Saint Maximus the Confessor defended the Latin use of the Filioque clause as a development of Western Christian theology. Then there is the Immaculate Conception; to argue such a doctrine is pagan is a Protestant argument: in addition both Orthodox and Catholic believe Mary never committed personal sin. As for papal infallibility, the Church Fathers spoke on this too: “Rome has spoken; the case is closed” (Saint Augustine, Sermon 131:10).
The point is there seems to be a paradox in common Orthodox beliefs regarding ecumenical councils and the Catholic Church. It is one which makes you question if the schism is not a schism or vice versa. Rebuttals against the Church from the Orthodox are trivial: e.g. Filioque clause, the use of unleavened bread for consecration into the Body of Christ, etc. These are non-issues and this is once again the irony of Orthodox anti-Catholic arguments: some Orthodox lament what they see as the Latin Church’s encroachment on the way the Eastern Churches do things, but do the very thing they accuse the Roman Church of doing.
Like I’ve said earlier Catholics and Orthodox have contributed to the schism, but in the end the Orthodox will need to accept the pope as the Vicar of Christ, that he is infallible ex cathedra when speaking of doctrine on faith and morals, that Mary was conceived free of original sin, etc.