Their only non Israeli route out is Egypt and Egypt doesn't want them. Egypt is even sending military to their border with Gaza to keep them out.
Egypt is moving to avert a mass exodus from the Gaza Strip into its Sinai Peninsula, as Israeli bombardment halted crossings at the main exit point from the Palestinian enclave on Tuesday, Gaza officials and Egyptian security sources said.
www.reuters.com
The sad truth is while you will see protest in Arabic countries and Arabic leaders have harsh words for Israel over this issue, none of them want them. Partly, because countries who have taken Palestinians in previously have had problems with them. Jordan, Lebanon, and Egypt have had a minority of Palestinians cause problems in their countries.
See the following for Jordan
en.m.wikipedia.org
Palestinians in Lebanon were using the country as a staging ground to launch attacks on Israel without the consent of the Lebanese government which led to Israel to start attacking Lebanon. Egypt has seen many of them join the Muslim brotherhood. They haven't been the best houseguests and now other Arab countries are
of any talk of importing them en massee. Like I said Arabic leaders got a lot of talk of support for them but it's all performative for internal politics for their pro-palestinian population. They aren't trying to do anything to actually help them.