Hi,
What they told you does make some sense, but it is really based on the condition of the present fluid. If the fluid is extremely dirty or smells burnt, you may want to leave it alone. If it isn't too dirty, you should be fine.
The idea that being extremely dirty makes a difference is based simply on this. The dirty fluid has all the friction material mixed in with it, so it helps prevent the transmission from slipping. New fluid has a detergent in it that washes that away. As a result (at least in theory), the cleaning leads to slippage.
If you are going to do it, here is a guide that will help with it:
https://www.2carpros.com/articles/how-to-service-an-automatic-transmission
As far as the differential, I don't feel that would be as much of an issue.
https://www.2carpros.com/articles/differential-service
Let me know what the fluid looks like and if you are presently experiencing any issues. Also, if the fluid smells burnt, that is often the result of low line pressure allowing the clutches to slip. Ironically, the pressure can be affected by dirt.
Let me know what I can do to help.
Take care,
Joe
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Saturday, November 27th, 2021 AT 11:38 PM