the muslims though did not call it palestine, nor were there any such people who were called palestinians during roman time, philistines i believe. the area has been called numerous names throughout history, but i specifically refer to the muslim claim. if they really want to go back a couple of thousand years in order to prove their "claim" on the land, then i would posit the jews would have them beat historically.
the reality on the ground is that the ottoman empire sided with the loser in a war, the land was lost. muslims claim ownership of the land after they took it by force over a thousand years ago. they have now lost the land because they sided with a loser during war. if you they can claim it by force of war, then then can lose it by force of war.