Personally, I'd say you just apologise for misunderstanding their intentions, politely inform them that the new feature is going to cost extra, and then suggest that, due to the misunderstanding, you're going to reduce your price for that implementation to $X, where $X is either the price you actually have in mind (if you don't mind being less than 100% truthful for the sake of fairness) or a slightly lower price (if you're willing to pay for their mistake so as to maintain more truthfulness). Yes, it can be hard to admit to mistakes you didn't actually make, but it's often necessary to not piss off some people.