Where did St Cyril say this? I am not saying that you are wrong. But there was a Byzantine (ie Orthodox) church or chapel on the Temple Mount too: http://orthodoxwiki....unt,_Jerusalem)
Most of the christian temples date to the time of Constantine and have been rebuilt whenever they were destroyed. The Justinian church only lasting 54 years, further verified the curse of the temple mount, as it was not rebuilt between 614 ad and 637 ad wqhen the city was recaptured and in christian hands.
... Now, since the true Christ is to come a second time, the adversary, taking occasion by the expectation of the simple, and especially of them of the circumcision, brings in a certain man who is a magician, and most expert in sorceries and enchantments of beguiling craftiness; who shall seize for himself the power of the Roman empire, and shall falsely style himself Christ; by this name of Christ deceiving the Jews, who are looking for the Anointed, and seducing those of the Gentiles by his magical illusions.
But this aforesaid Antichrist is to come when the times of the Roman empire shall have been fulfilled, and the end of the world is now drawing near....
And again he says, Who opposeth and exalteth himself against all that is called God, or that is worshipped; (against every God; Antichrist forsooth will abhor the idols,) so that he seateth himself in the temple of God. What temple then? He means, the Temple of the Jews which has been destroyed. For God forbid that it should be the one in which we are! Why say we this? That we may not be supposed to favour ourselves. For if he comes to the Jews as Christ, and desires to be worshipped by the Jews, he will make great account of the Temple, that he may more completely beguile them; making it supposed that he is the man of the race of David, who shall build up the Temple which was erected by Solomon. And Antichrist will come at the time when there shall not be left one stone upon another in the Temple of the Jews, according to the doom pronounced by our Saviour; for when, either decay of time, or demolition ensuing on pretence of new buildings, or from any other causes, shall have overthrown all the stones, I mean not merely of the outer circuit, but of the inner shrine also, where the Cherubim were, then shall he come with all signs and lying wonders, exalting himself against all idols; at first indeed making a pretence of benevolence, but afterwards displaying his relentless temper, and that chiefly against the Saints of God..: (Catechetical lecture xv)