The term likely arose because mechanics often get their hands dirty with grease and oil while working on cars.
The term can be used in a neutral way, simply referring to a mechanic, or it can be used in a derogatory way, implying that the mechanic is unskilled or dirty.
Here are some ways the term might be used:
* Neutral: "My dad was a grease monkey all his life."
* Derogatory: "That guy is just a grease monkey, he doesn't know anything about real engineering."
It's important to be aware of the context and tone when using the term, as it can be perceived as offensive by some.