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Make sure they guarantee this will fix it, it really sounds fishy to me. I think they just neglected to re-train the IAC when they had the battery disconnected to do the other work. The vehicle needs to be started within (15) minutes of battery re-connect to start the training process of the IAC, new or old, then driven under various conditions including much idling to train it.
The only thng they have in common, is when the battery gets disconnected, the IAC needs to be re-trained.