OK. I thought and a Google appears to confirm that the Egyptian border is closed to goods. As for people if would appear that they can stay in Sinai for fourteen days and that's that. I don't think we can assume that Palestinians will be able to find safety in Egypt.I can't find where I saw it I'm afraid. But Israel does not control the border crossing to Egypt.
I imagine Palestinian refugees will have an easier time crossing the Egyptian border than the Israeli one.