Q: I had my rear differential replaced but it did not fix the noise problem. on 2004 Cadillac SRX

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Now the mechanic wants to do some other things, like change the transfer case. Should I get a refund for the work that did not work? He is the one that said what needed to be done.
(1) Answer
he needs to provide some sort of proof that there was a failure. if he made a bad diagnosis, then he is responsible for that mistake, not you. I would get the car out of there and go somewhere else and get a correct reason for your noise.