Transman beat me to it. I was thinking the very same thing about the 3rd shop. Either something was misinterpreted or misheard, or they’re outright telling falsehoods, but there is no pan to drop on your transmission. That would be like me telling you your chimney needs repair when your house has no fireplace. Stay away from them.
Without knowing the specific fault codes you had, hard to tell what the trouble is, but unless it can be repaired with an externally accessible solenoid, it’s likely to cost you $2-3K.