Resolution:
1) To remove access to the recording so that the owner is the only one that has access, follow the steps below.
2) Open Microsoft Stream by clicking HERE
3) Open the video that you want to change access to
4) On the right side of the screen, you will see a button that says 'Share'

5) Click on the bottom option that says 'Manage Access'

6) Click on 'Stop Sharing' at the top of the window that pops up

7) Close out of the Manage access window when done

8) Once this is done, only the owner will have access to the recording.