According to the synoptic gospels "Not one stone of these buildings (plural, the Temple itself was singular but Christ is referring to the entire Temple mount) will be left unturned" however the western wall of the Temple Mount still remains. So either these Prophecies are false making invalid the synoptic gospels or the wall is not authentic which would mean there is no rightful claim by anyone to this area and praying on this would be idolatry.
- rebdobr