Each video in your Watchlist has a blue "X" located in the upper right side of the video. Click the X to delete the video. You cannot recover a video that has been deleted; you must locate the video again and add it to your Watchlist.
If you do not see the blue "X," simply open a browser window and go to pbs.org. Log in using your account username and password, navigate to the Watchlist, then remove the desired programs by clicking the "X".