I finally called Apple Support to get the answer to this question.
1st, make sure you are signed in on your computer under the Apple ID that purchased the movie.
2nd. Go into the summary page of your device on ITunes. Near the bottom you will see "options". In that section you will see "manually manage music and videos". Select that option.
3rd. Then go to the "On this Phone" click the RENTAL sub section under your device. This depends on the version of ITunes you are using.
4th. Right click the movie you want to delete. The popup box with the delete option should appear.
5th After it deletes (which will take quite a while) remember to go back into Options and uncheck the option for"manually manage music and videos". ℹ🙂