If they're asking for a cut to shop and help close the deal then they're playing banker. That's the kind of thing bankers do. It would blow my fucking mind if they wanted a cut to shop their own exit. If that's the case you should be profoundly distrustful. Either way lawyer lawyer lawyer.
Unless, as someone mentioned above, they invested just a little bit and this deal will be making fortunes for others AND they are putting huge efforts into the deal process.
In this case they are acting as a banker who happens to have a stake. I don’t like it but if you compensate them based on uplift from the proffered term sheet then that might be palatable.
But if they are trying to stall the deal unless they get paid then charitably they may be saying this is a premature and under market price and they are only happy, if the founders want out, to get their return through the top up. Uncharitably they see they can stop the deal and have negotiating power and are screening everything until they get paid.
Overall a deal needs everyone to smile to get done. If they make you a lot more money over the offer then it’s ok to make them happy - as long as all shareholders agree.
If they just need a kicker to make everyone else happy then you might need to grimace and pay, and I imagine sign an NDA. That’s not a great way to do deals but it is an exit.
(VC - and we never charge the companies anything)