No way a properly repaired engine should take a gallon. They should have purged and/or vacuum-filled it, just like the factory. Nobody expects to add coolant to a new car, that cooling system is properly filled and the new engine isn't leaking coolant.
They either did a terrible job, or it's leaking coolant into the combustion chamber and burning it. A competent mechanic will check for exhaust gases in the coolant (my guess, that test will come back positive, and you need, at the minimum, new head gaskets).
If it's leased, do you have to keep adding coolant? Isn't that task a part of the repair?
What would happen if you simply drove the car, as you should be able?
When the engine overheats/blows up from a lack of coolant, would they fix it again?