How do you delete a movie from the "Recently Watched" list? Is this possible?
Not possible. That has been asked a bunch. (Often due to soft porn that the watcher did not want others in his/her household to know about.)
What you can do, as RokuShawnS implied, is watch several shows and it will go away. You do not need to watch the whole thing, just start it and run a few seconds and it should join the recently watched list and bump the oldest off. It does need to be 10 different shows however.