This banner ad was bugging the hell out of me too. I figured out how to remove it, but this might void your warranty or whatever so do this at your own risk:

1. Close Ubuntu Software Center and make a backup copy of
   
   /usr/share/software-center/softwarecenter/ui/gtk3/widgets/exhibits.py




2. Edit that file as root:
   sudo gedit /usr/share/software-center/softwarecenter/ui/gtk3/widgets/exhibits.py




3. Find the line which defines MAX_HEIGHT = 200 (line 229 or so)




4. Change MAX_HEIGHT to 10




5. Save the file, restart software center, banner no longer obtrusive.