Why does the replacement starter grind briefly after the engine starts?

Hello,

It sounds like the new starter is staying engaged longer than it is supposed to. Likely due to internal fault.
So, this will need to be replaced to prevent damage to other components like the flex plate.

Was this installed at a shop, or did you install the starter?
Either way it should be covered under parts warranty.

https://www.2carpros.com/articles/how-to-replace-a-starter-motor

Let me know of any questions.
Thank you.

Yes, it was installed at a franchise place, I came back and told them the problem, they said it was the old starter's fault and did nothing, but I don't believe it. May travel to a different area shop same name, as I believe that the warranty is good for any shop of theirs. And try to deal with a different set of people. Could it just be the solenoid?

It could be the Bendix that is sticking just enough to create the grinding noise. On these starters the solenoid and the starter comes as a one unit.