If Jews are currently prohibited by Torah law to set foot on the Temple Mount because we don’t know the precise location of the Holy Temple, does this mean we have to give it up to the Arabs (who literally treat it like trash)? Why or why not?

ב"ה Shalom Indeed, the entrance of people who are forbidden by Halacha to do so is heartbreaking. However, these are issues which are connected to our political situation in the world. On the other hand, we have to look at the bright side, that after 2000 years of exile, the sovereignty over the Land of Israel is Jewish and the ruler of the Temple Mount is the State of Israel with all the shortcomings you mentioned. These shortcomings do not diminish our reverence for the sanctity of our the Temple Mount. All the best I