Audi Repair Questions? Ask a Mechanic for Answers ASAP
That engine package is a little louder than some comparable vehicles but the fact he/she can feel it is concerning. It is possible since it goes away on coast that it is a loose or failed engine mount allowing the engine vibration to transfer into the chassis/shifter. If you are serious about this vehicle I would probably have a service facility look it over on a lift, check all fluids, and investigate the noise further. Since the inspector is limited to ground inspection and test drive only. If it is a mount, it might be fairly apparent on a lift.
Different expert here
I suspect that this is in the drivetrain, possibly a transmission gear issue. I know this can be a pain, but can you ask the remote inspector to retest drive and when it is making the noise, to shift it to neutral and see if the noise immediately disappears or not.