I downloaded and looked at the User Guide. There is nothing about any sort of eraser tool found. Is your older versions Photo Express or perhaps one of Ulead's other programs? PE seems to be a rather simple and basic programs, that would not have the ability to erase parts of the background.
If you're wanting to do that, you might download the trial version of PhotoImpact X3.
I downloaded the trial version and played around with it. Sorry to say that I confirmed my suspicions. You can not erase any part of the image that you did not add. I even tried duplicating the image, and still it would not permit erasing it.