As you see the starter makes this noise when it is not engaged in flywheel (over running clutch is ruled out)
The only thing is left unchecked is the planetary gear set and the starter sounds like my old DeWalt cordless drill as it stops.
The rebuild Autozone starter I took apart on the wrecking yard had liberal amount of grease added to the planetary

Ring gear and carrier

while previous starter from overturned car had black goo on the gears
Looks like grease makes a trick (but won't help if bushings are messed up)

 

My 07 CRV made that grinding noise for years at a cold start. It did eventually fail, but thankfully you get a pretty good heads up when it is getting close to the end.. My Fit does it as well so it'll only be a matter of time.