FWIW, I’ve a relative who dislikes fish, but who often makes an exception for local fish & chips. Locally the preference is for haddock which is what’s generally served, and what that relative gets.
The same relative is less fond of cod, so I guess the advice there, if any, is if you try cod and don’t like it, try haddock. Or vice versa.
If the pricing is itemised, you could price the impossible feature at an exorbitant rate.
Either way, has your company previously sold this feature or is this just a mistaken belief about the existence of the feature that the customer has somehow invented themselves?
If the feature isn’t on any of the customer’s previous itemisations and they’re the ones who made it up accidentally, suddenly seeing it on a new itemisation with a sky-high price tag might make them realise without explicitly telling them, which may or may not be what you (as the individual) want. I assume your boss will get wind of this one way or the other, so you could get them on-side by suggesting this idea.
Is this feature something one of your company’s rivals might be able to implement or is this one of those situations where the feature would literally break the laws of physics? (Or mathematics, etc.) If the latter, it might be easier to come clean to the customer with a full explanation. If the former, your company needs to get on R&D immediately. Consult experts in the field. And that’s where the exorbitant rate comes in.
How much of this your company shares with the customer is down to your chain of command. How much you share with the customer is down to how much it will affect you personally one way or the other.
Lots of ifs, buts and maybes here. Good luck. I think you need it.