I feel like you should name and shame, to some degree. Ask the VC for a reference to another portfolio company who had this arrangement. Or, cold email their other founders and ask if they
have this arrangement. Email any other investors you have to ask whether this is ok. My guess is that the investor knows they are being greedy, and they know that their reputation would get hurt if others knew they were doing this. If it's not a shady action, then I think nobody will fault you for asking around.
I don't necessarily think the VC has bad intentions. But, it sounds like they are trying to change the terms of an existing agreement. That, to me, seems unethical. Talking about these shady actions publicly tends to cause the community to self-police a lot. Perhaps another investor will inform this VC that they make money now, but hurt deal flow later, by taking actions like this.
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One other thought: you could say something like "the company lawyer says this is not a normal arrangement and wants specific paperwork due to SEC deal maker rules. Can you have your lawyer send us the proposed agreement?" My guess is that they will drop it then they realize it will cost $10k in legal fees to do this, and it might even be illegal to do contingency fees without being a registered deal maker with the SEC.