if I take a hoop/window and place it quickly over an object
Then the velocity of the object relative to the “exit” of the hoop would be the same as the velocity of the object relative to the “entrance” of the hoop, which is option B.
In your analogy, option A would mean the object has a relative velocity of entering the hoop but suddenly no relative velocity exiting it, so the object magically starts following the hoop.