Muhammad's tomb is located under the Green Dome of Al-Masjid al-Nabawi in Medina.
Photo Credit: Wikipedia

One argument I read often on forums is that the Jews should get out of 'Palestine,' that it is not their land. This assumes that Jews are recent arrivals to Israel.

Actually, there has been a Jewish presence in Israel and the Middle East for two thousand years. Jews even dominated this part of the world for centuries until Mohammed came along and set off mass slaughters, conversions, expulsions, extortions and expropriations of their property.

Before it became Islam's second holiest site and off limits to infidels, Medina was a Jewish-controlled city:

Bernard Lewis, The Arabs in History,
Page 40

The city of Medina, some 280 miles north of Mecca, had originally been settled by Jewish tribes from the north, especially the Banu Nadir and Banu Quraiza. The comparative richness of the town attracted an infiltration of pagan Arabs who came at first as clients of the Jews and ultimately succeeded in dominating them. Medina, or, as it was known before Islam, Yathrib, had no form of stable government at all. The town was tom by the feuds of the rival Arab tribes of Aus and Khazraj, with the Jews maintaining an uneasy balance of power. The latter, engaged mainly in agriculture and handicrafts, were economically and culturally superior to the Arabs, and were consequently disliked.... as soon as the Arabs had attained unity through the agency of Muhammad they attacked and ultimately eliminated the Jews.

Jews in the Peninsula of the Arabs who were not killed, converted or enslaved were expelled to fulfill Mohammed's deathbed command: "Let there not be two religions in Arabia."

Here's the interesting part: they were resettled on lands assigned to them in Syria and Palestine. That's right - the Jews were sent to Palestine 1400 years ago on the orders of Allah's Last Prophet on Earth.