Does a repair garage have to supply the customer with a copy of how muchit paid fora replacement part?

This question is best asked by an attorney admitted in Vermont for specifics as the law.  But generally speaking a consumer is entitled to an itemized bill for repairs made to their cars and that would include the cost of the items that were replaced in their car.  It seems to be a valid request to me as well.  I am assuming that you think that you are being charged a mark up for the transmission, correct?  You may want to call the State Attorney Generals Office Consumer Affairs Division to ask for help here.  They may be able to guide you in the right direction and even take on your cause here.  Good luck.  

There is no law generally requiring any business to show customers the cost of its parts, inventory, etc.

In the event of some billing dispute--where either the customer doesn't pay and you sue her; or she pays, but then concludes she was defrauded and tries to sue you--during a lawsuit, you might be forced to provide this information if it is relevant to the suit in some fashion. That's because in a lawsuit, through the mechanism of "discovery," it's possibly to obtain almost any documents or information that is germane and relevant. But short of a lawsuit, you do not need to provide or turn over this information. That doesn't mean you can't, if you decide to; but you are not obligated to do so.