it's possible that it's your player itself that is doing this. and not the backup software. clonedvd2 cannot put something on a disc that isn't in the files that you've specified for it to burn.
my guess is that for some reason your dvd player or tv and holding onto a clip. is the clip from the previous movie that shows up always the FIRST thing you see before you get into the new dvd that you've just burned?
is the clip generally from where you left off watching the previous movie?
i've never experienced this on dvd, but i used a dv-cam player at school that kept the last frame it played visible until the next tape was inserted. i walked into the lab to do a project once and got a funny scene ofa classmate and his girlfriend in an uncompromising position. apparently he was viewing/editing his "home movies" in the school labs and was unaware of the frame holdover haha.