Wrong. Israel will stamp a separate piece of paper to leave in your passport during your visit for exactly this reason.

Having records of a their Israeli degree all over the internet is probably a bigger problem for somebody intending to return to Iran at some point in the near future, even if only just to visit.

Iranian government has spies everywhere and keeps pretty comprehensive lists of citizens they don't like and will harass them and throw them in prison, or executive them, on a whim when they try to re-enter.