Just make the stamp unreadeble

It's possible to soak the passport overnight in cold water, then remove the offending stamp with babywipes.
Obviously that'd be illegal so I don't recommend it...

Hmm. I would really advice AGAINST manipulating the stamps of your passport as this would make your passport unvalid. Changing stamps is a nasty bussiness. I was accused of chaninging my azeri stamp in Azerbaijan once (witch I had not done) and they initially refused to give my passport back. As a kid I drew stamps on my own in my passport, and my parents had to get a new one.
Since Iran has an issue with "the occupied palestine" (meaning Israel) you should not try to hide the stamps. Better to get a new passport.
Say to your embassy that you whant a new parallel passport to go to Iran. Sweden I know issues an extra passport if you say that you need it to go to Israel. Maybe you can arrange something similar.

A second passport is good for this only if it is absolutely identical to the original one in every respect. Otherwise, the Iranian authorities will know there is a first passport and will demand to see it. Remember: They don't have to prove anything. If they just suspect that you have been to Israel they will deny you entry.

Obviously josef_sv is right about manipulating stamps being a little risky. What I said was true (I've seen it done), but I'd avoid doing it myself!
The tone of some posts (a1 for example) seem to imply that Iranian border guards are pro-active about looking for people who've been to Israel or caused some other opffense. Personally, I only ever cross the border at Razi so I cant speak for the airports, but all they ever do with me is check my visa, and give me an entry stamp.
No questions, no search, nothing. It's all very straightforward.

#14
The tone of some posts (a1 for example) seem to imply that Iranian border guards are pro-active about looking for people who've been to Israel
========================================
You are correct because what we have written is what actually happens: They're actively looking for the possibility that travelers have been to Israel. The same when entering Syria or Lebanon. They check your passport very carefully to make sure there isn't even a hint that you've been to Israel.
...and not only in your passport. A receipt from a Tel Aviv restaurant is as much a giveaway as any passport stamp.

@a1:
OK, if that's your experience then by all means share it, Like I said, I have no experience of using the airports, only the Razi land crossing (from Turkey). Maybe they treat people differently because I have have never experienced any kind of interview or bag search when entering this way. It's totally relaxed, if a little dull.
It just strikes me that there can be a little hysteria around entering Iran, regarding clothing, borders, local customs etc, and it's worth resassuring people that they're not entering the dragons lair...

#17
It just strikes me that there can be a little hysteria around entering Iran, regarding clothing, borders, local customs etc, and it's worth reassuring people that they're not entering the dragons lair...
============================================
Where is there hysteria? Who hinted anything about a "dragon's lair"? A question was asked as to how the Iranian authorities check your passport for evidence of having been to Israel, and we answered that question. No more, no less.