Maybe a reduced price for a smaller yard is a more sensible rationale.
Get your original contract out and check if a survey was part of that contract...or a legal title....then get an attorney to send a love letter to the contractor with a price reduction....or just talk to the contractor first...make an aggreement on adjusted price and then send a letter confirming the change.
My other question as a Realtor who represents buyers and builders is "How important was that 6 ft in the yard?" Does this keep you from doing something in particular that is an insurmountable obstacle in purchasing this home otherwise? Or is there more?
Do you have a Realtor representing your interest?