Busdaddy listened to it and he thought it might be something to do with the flywheel, as well, but evidently had never heard that sound before, so his response wasn’t nearly as knowledgeable as yours.
So. At this point, do I take it back where I got it and have them install a new one while I wait? I can’t see me paying my mechanic twice for the same job. He’s too much of a keeper to cause any dissention!
Not just a little swam gas then?
I'd suggest a phone call. Tell them you suspect the starter is not pulling away properly after releasing, and ask if there's any way they can rectify it.
A skilled mechanic, with some luck available, might be able to shim the starter to eliminate the noise.
Worst case, another starter. Somebody needs to cover the labor.