Looking at this only from the viewpoint of the customer and assuming the work you did was exactly as described on the contract.
If you want to do a bit of extra work just to make the customer happy, then yes, lower the sod a bit, but get the agreement it in writing or this could go on forever. A satisfied customer is your best form of advertising.
On the other hand, if you give the customer an estimate for the cost to remove sod, dig a trench, install a French drain, replace the sod (or go with the gravel/stone option), which would involve an entirely new contract, I don't think the customer would be pleasantly surprised. And since you would be doing the job while walking/digging/hauling on the lovely new delicate sod you'd need to take precautions not to "damage" the sod.
