As did other dominant groups before and after them. In any case the Jewish population's size and influence peaked after a major catastrophe (the Bar Kokhba revolt) some 500 years before the first wave of Islamization even reached the region.
Isn’t this just manufacturing an artificial claim?
What they did was no different from the inevitable self-imprinting both religious movements and settler groups do in places the get traction in - they started to believe in a part-mythical, part factual "origin story" of how they got there and assumed dominance, and that was that. In essence no more "artificial" from the imprinting of any other group that attains dominance in a region over time (including that of the Jews in the area, many centuries previously).
Islam's telling to itself seems to go about like this:
https://en.wikipedia.org/wiki/Religious_significance_of_Jeru...
By way of context: (1) it took a long time for this to happen (specifically in two waves about 550 years apart), and (2) even by the first wave, the Jewish community had already been vastly diminished (in part by expulsion, in part by assimilation as the other commenter notes), and the region had already been long since Christianized.
So there was no major Jewish imprinting to dismantle or oppose by then - or even make reference to, by then. If anything (with Christianity's imprint melting away before them) the region probably started to appear as a tabula rasa to them, in short enough order.
https://en.wikipedia.org/wiki/Siege_of_Jerusalem_(636%E2%80%...
Also, it wasn’t just Jewish people who lived in what is now the territory of Israel in ancient times - it always had a significant population of polytheists (Canaanite, Phoenician, etc), plus two thousand years ago the Samaritans were a massive community of military significance, not the tiny minority they are today. Most of its non-Jewish population converted to Christianity - along with a significant chunk of its Jewish population. And then when Islam came along, the majority of its Christian population converted to Islam (a slow process over many centuries). Arguably, Palestinians are just as much descendants of its ancient population as Jews are, indeed, Palestinians are likely in part descended from Jewish converts to Christianity and Islam.