I can't answer the question directly. But, to my knowledge Israel usually stamps a separate piece of paper vs. a page in your passport because of issues like this with its neighbors. And, Israel is later in your trip anyway, right? So, your passport should be fine if inspected.
Is there anything in your documentation that makes it clear you are traveling to Israel or have visited there before? Your flight out of BEY is probably not going to Israel, so a clean passport and a boarding pass to someplace else should get you in and out. But, I'll defer to folks who have done this at BEY.