Dr Henry Chadwick relates this in his seminal East and West: The Making of a Rift in the Church:
"We owe to Syropoulos a touching description of the pain felt by the Greeks as they looked at the walls of San Marco in Venice plastered with Greek loot from St Sophia at the time of the Fourth Crusade. These treasures in the west had been stolen by barbarians." p.265.Not one of the Greeks could actually have remembered the "loot" that was stolen, the horses of St Mark, for instance, plate and vestment, and doubtless other treasures of worth. The Greek retinue passed through Venice when the Council of Ferrara was in session, over two centuries after the Fourth Crusade. Nevertheless they would have remembered those things in song, much as Gimli and the rest of Durin's folk remembered their antient mansions at Hadhodrond (which became Moria in its darkness), though they had never seen them. As Tolkien says:
"'I need no map,' said Gimli, who had come up with Legolas, and was gazing out before him with a strange light in his deep eyes. 'There is the land where our fathers worked of old, and we have wrought the image of those mountains into many works of metal and of stone, and into many songs and tales. They stand tall in our dreams: Baraz, Zirak, Shathûr.May you have joy of the sight...
'Only once before have I seen them from afar in waking life, but I know them and their names, for under them lies Khazad-dûm, the Dwarrowdelf, that is now called the Black Pit, Moria in the Elvish tongue. Yonder stands Barazinbar, the Redhorn, cruel Caradhras; and beyond him are Silvertine and Cloudyhead: Celebdil the White, and Fanuidhol the Grey, that we call Zirakzigil and Bundushathûr.
'There the Misty Mountains divide, and between their arms lies the deep-shadowed valley which we cannot forget: Azanulbizar, the Dimrill Dale, which the Elves call Nanduhirion.'
'It is for the Dimrill Dale that we are making,' said Gandalf. 'It we climb the pass that is called the Redhorn Gate, under the far side of Caradhras, we shall come down by the Dimrill Stair into the deep vale of the Dwarves. There lies Mirrormere, and there the Rilver Silverlode rises in its icy springs.'
'Dark is the water of Kheled-zâram,' said Gimli, 'and cold are the springs of Kibil-nâla. My heart trembles at the thought that I may see them soon.'
'May you have joy of the sight, my good dwarf!' said Gandalf." The Lord of the Rings, Book II, Chapter III.
Later, after the Fellowship hardly passed through Moria, they were guided into the fastness of Lothlórien, and were summoned to the lord and lady. Galadriel, holy and queenly, then said, as though she had read Gimli's mind from afar:
"'Dark is the water of Kheled-zâram, and cold are the springs of Kibil-nâla, and fair were the many-pillared halls of Khazad-dûm in Elder Days before the fall of mighty kings beneath the stone.' She looked upon Gimli, who sat glowering and sad, and she smiled. And the Dwarf, hearing the names given in his own ancient tongue, looked up and met her eyes; and it seemed to him that he looked suddenly into the heart of an enemy and saw there love and understanding." Ibid, chapter VII.What a pity that when the Greeks, impotent, isolated, desperate and yet with the memory of greatness, came into the West they encountered no such love or understanding but lofty contempt and suspicion. What a pity they had no joy of the sight of their antient treasures as the Venetians croaked in mockery. What a pity that, under imperial pressure and compromised by Italian hospitality, they signed up to a union that deep in their hearts they loathed and despised. What a pity that this false union availed not to stem the ineluctable Turkish tide, and that God's judgement was revealed most clearly in the victory of Christ's enemies on that dreadful day in May 1453. What a pity that the mighty Roman king fell beneath the stone, a schismatic.
Still, where the Greeks have failed, the Russians have taken over.
 This last seems to echo Gimli's song in Moria. One wonders about the reach of Galadriel's thought.