Have a look at how mining pools are implemented. The client only gets to change some part of the block and does the hashing from there. You can't go back from that to change the original data - you wouldn't get paid. Otherwise you could easily scam the mining pool and always keep the winning numbers to yourself while getting paid for the partials too.
Just to make sure I understand this (and maybe clarify for others too), because my understanding of proof-of-work systems is very high level:
When you mine a block, you’re basically bundling up a bunch of meaningful data, and then trying to append some padding data that will e.g. result in a hash that has N leading 0 bits. One of the pieces of meaningful data in the block is “who gets the reward?”
If you’re mining alone, you would put data on that block that says “me” as who gets the reward. But if you’re mining for a pool, you get a block that already says “the pool” for who gets the reward.
So then I’m guessing the pool gives you a lesser work factor to hit, so some value smaller than N? You’ll be basically saying “Well, here’s a block that doesn’t have N leading zeroes, but does have M, leading zeroes”, and that proves how much you’re working for the pool, and entitles you to a proportion of the winnings.
If you changed the “who gets the reward?” from “the pool” to “me”, that would change the hash. So you can’t come in after the fact, say “Look at that! N leading zeroes! Let me just swap myself in to get the reward…” because that would result in an invalid block. And if you put yourself as the reward line in advance, the pool just won’t give you credit for your “partial” answers.
Just to tack onto this, the one thing you could do is just deny real rewards. If someone wants you to take part in their pool in order to load a webpage, you could just refuse to submit any block that will actually pay out. This wouldn’t benefit you, but it would punish them for trying to make you spend resources on their behalf.
