To all of the good advice that has already been given, I will add that you have illustrated the typical problem that people encounter after using a quick lube place.
Due to poorly-trained, time-constrained teenaged employees, coupled with an "up-sell" philosophy, quick lube places are rarely cheaper than a real mechanic's shop would be for the same service, and they are MUCH more prone to making fatal errors. Each month, we read a few posts from people whose (pick one or more) engine/transmission/differential/brake hydraulic system/cooling system was damaged or destroyed by the employess at Jiffy Lube or one of its clones. Now that you have learned your lesson the hard way, please be sure to AVOID these quick lube joints with your next vehicle.
However, as andrew j pointed out, the book value of your car is such that nobody would be likely to pay for transmission repair or replacement, and a check for the car's book value is probably the most reasonable settlement. That being said, I really doubt that the computerized invoice states something like "we removed 3 qts. of transmission fluid". If the invoice does state something to that effect, then you can probably prevail with a claim. In the absence of hard documentation, this may wind up being a REALLY expensive lesson in why you should not use a quick lube place.