Mandatory Palestine was what that map calls “Jewish Palestine”, not Trans-Jordan. Note that Trans-Jordan was explicitly not included.
This whole thing is really just a rabbit hole, at least for me. And a very complicated one steeped in geopolitics, world war, balfour, etc.
For me, it’s similar to arguing the Indians having claim to land in the US. The 20th century, by the end of WWII, pretty much put an end to how land was conquered for the history of mankind, even before we started building walled towns.
The history is interesting, but has little power to enforce changes to modern claims. And no, the Indians (or “native Americans”, as some prefer) are not getting any land back. I think the best thing that could happen to them, long term, is the abolishment of all land treaties and fully absorb them into the states they are currently in. Maybe that would pull them out of the abject poverty that they enjoy so much today.
But, of course, the treaties are sacred. And their leadership is a bit xenophobic.