“Would Egypt ever take Gaza back?”
I believe none of the Arab world wants the “Palestinians.” Those who went to Jordan have been a constant destabilizing force. It would be like a nice neighborhood in your town importing a bunch of MS-13 members. So, the answer is no.
Egypt has purposely flooded Palestinian tunnels between the territory and Egypt. Egypt has been fighting an anti-terrorist war in the Sinai. Egypt even allows Israeli drone and airstrikes there. Israel shares drone intel with Egypt.
So-called Palestinkians were thrown out of every Arab country. When the UN divvied up the ME, they set Jordan to be the Palestinkians home, not Israel. The only problem is they tried to overthrow the King and got their behinds handed to them, royally, as they lost 80K Palistinkians in the incident. Now Jordan and Lebanon both have dirty, dirty, Palestinkian refugee camps which each hold more than all of Israel. In Israel, the Palestinkians are allowed to be a voting member of the Knesset and allowed to vote in the elections. They are considered citizens of Israel. Compare that to Lebanon and Jordan where Palestinkians are not allowed to leave the camps and utilities are not allowed in the camps. The Iranians and other Arab countries use the Palestinkians in their proxy war against Israel.
Palistinians = human cockroaches.