Corolla making strange noises

[LeNeve]

The second thing is they said that the right transmission arm has a coupling (not the word he used but I can't remember the exact word) and it looks like it is "throwing grease." He said he didn't know if it could be replaced or if the entire transmission arm would have to be replaced.
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That's the axle (halfshaft) and the constant velocity joint boot. Replacing those is not out of the ordinary on a FWD car with that many years on it. If something tears the rubber boot that covers the CV joint it will lose the grease and collect dirt leading to eventual failure. Not a big deal to replace. Just do both sides at the same time.

I agree.