Israel occupies lands belonging to the Biblical patriarch Jacob. That was something like 1800 BCE, two and a half millennia before Mohammed. Islam refers to Jacob, as does the Torah/Old Testament as "Israel".

I find the repeated suggestion that those are Muslim lands because Israel is a new territory to be strange -- it can't be a Quranic position. It doesn't appear consistent with history either.

That's a ridiculous position. We can't organize today's world based on who was where 4 millennia ago. (If we did, most if not all countries would immediately cease to exist, starting of course with the US but not limited to them.)

Assuming this claim were true, which it isn't, the modern Israelis have genetically nothing in common with the Jews of the old testament. They don't have the same culture, religion, language or genetics.

I find historical claims like this not very convincing. 1800 BCE looked very different from today and if people from old civilizations start claiming their land, we would not see any end of wars. Should Italy claim most of Europe because Romans had it under their control?

You make it sound like the dispute is about who has some ancient religious right to the land. It's true that both sides claim that but it's totally disingenuous to pretend that is the reason for so much Arab anger.

People still have a living memory of specific properties in specific locations that they were forced out of and are now occupied by other families, often with some of their relatives killed in the process That applies both to places in Israel proper (displaced in 1940s to 1960s) and to Gaza and the West Bank (in the time since then). Even before the most recent war in Gaza, any Palestinian could be forced out of their home at any moment by an Israeli settler with no recourse.