Carl, could you please explain which "border around the banner" you mean.
In the meantime you can experiment with the interactive Moodle theme Chameleon to find out how to work with the CSS on certain areas of Moodle pages.
Simply experiment with Chameleon until you have achieved the change you desire, then copy the CSS in the "Free Edit" tab to your CSS file in your own theme.
I hope this helps
Urs