If you want to remove the border from the whole of the header section using css then thats easy. Just put this in your stylesheet somewhere
#punwrap #brdheader div.box {border: none}
If you just want to remove the border around the logo then it would be simpler to alter the markup as in this case the markup you need is in the template file main.tpl so you can just alter it and then style it however you like. There is a css way of doing it without actually removing the border. You just use a 1px negative margin on the logo container so it overlaps/covers the border
Don't assume that everything you want is in the css file. The stylesheet only uses what the default styles need. You have to add your own stuff if you want to do more than just play about with colours.
NOTE: If you do what Quaker says all that will happen is that the tables will end up with black internal borders.