I and several others here have complained about a grinding noise coming from under the car when 1st starting the car in the morning and shifting into drive or reverse. I suggested it sounded like a loose heat shield...well I have fixed the noise which I still think is a vibrating heat shield.
I just replaced the lower rear engine mount and the sound has gone. I think when the car was under load by putting it in gear the engine was moving enough to cause one of the heat shields to vibrate against something. Replacing the engine mount has stiffened up the engine and the noise has gone

 

I'll bet it feels good to have knocked that out.