I’m not sure in what sense Israel owns the Temple Mount now. As I understand it Jews can’t go there and pray. Seems to me Muslims already “own” it.
You are partly right, partly wrong...I visited the Temple Mount 2 years ago. Jews are allowed up there, but the Orthodox don't go because they do not want to accidentally desecrate the Holy of Holies by walking on it (since it is not known precisely where it was). Many Jews (Orthodox and otherwise) pray at the Western Wall and in the excavated areas that have exposed portions of the walls from Herod's time--not on the Mount itself.
Concerning prayer on the Mount: we (a group of Christians) were told not to pray in an obvious manner (folded hands, bowed heads, etc.) as we would be asked to leave by the Muslim police patrolling the Mount area if we did so. I assume the same would happen to any Jews who appeared to be praying.
Muslims think they own everything. They’re just waiting to take title.
By that measure, ownership could change in 30 seconds by simply deploying troops to seize control
The Israelis biggest mistake was to not just demolish the mosque when they captured the site