“Are you saying the the current Arab residents are not descendants of previous Arab immigration”
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Exactly, most are grandchildren from recent Arab immigration.
I was imprecise in my question. I had meant "previous" to mean all Arab immigration previous to the present day, not to distinguish more ancient immigration from more modern. It is irrelevant from which wave of immigration the present Arab population is descended, as if we could even distinguish such in what must be a highly mixed population. The point that I had wanted to make, in answering the question what these two groups have to do with each other, is that the descendants of both groups are now residences in the territory controlled by Israel.
The fact that some Arabs are descendants of a more recent immigration does not delegitimize their presence any more than the fact the the Jewish population is made up of descendant and actual members of a much more recent Jewish immigration. If you are going to discount the modern Arab immigration then you must do the same with the modern Jewish immigration. If anything, the Arab population pre-dates the bulk of the Jewish population.
It is useless for either side to seek to delegitimize the population of the other because of when they arrived. The land has a mixed Jewish and Arab population and neither is going anywhere. Both sides need to accept the population that is present on the ground today.