What do you mean a border? You probably have the resisable option checked for the Movie Properties. It appears as a border but it really isn't.
To make sure that it is not checked, here's what you do.
Click on an empty space in the score. This will allow the Property Inspector for the movie to be available.
Click on the "Display Template" tab, within that tab, uncheck "Resizable" if it is checked. Re-publish your movie.
Does this solve the border issue?