I have a 2001 Jetta TDI that has a rubbing noise coming from the under side, i think from the engine cover under the engine. This noise is only noticeable when decelerating in 2nd & 3rd gears at low speeds. When you push the clutch in, the noise goes away.

Suggestions, ideas, comments?

 

Could be the engine protector. Does it sound like plastic scraping? If you can get under it and see if any of the mounting screws are gone or if it is really scratched up then I'd say it's a good bet.