There re two types of quotes: binding and non binding.  One would have to see the paperwork you have in your possession.      Many things can vary as to the shipment estimate like the weight of the cargo container.  If the weight was estimated to be one tonnage and the actual weight is heavier then you can have a discrepancy.  I would go and find a legal services agency that can help you here.  And possibly contact the State attorney general for help.  Good luck.