I think it is an unintentional artifact rather than a purposeful line that can be removed. It's possible that saving it to a SVG file will give you the image you need. But that might depend on the software that renders the SVG. (SVG is a vector format rather than a pixel format and not all SVG rendering packages use the same rules.) PDF might also be a good choice.
It's also possible there is a preference (probably under windows-specific, try the hardware accelerated one) that might turn off the anti-aliasing behavior that might be triggering the problem. I suspect the rectangle borders are half way between pixels and the OS is fading the edge pixels toward the background color...maybe even on both adjacent rectangles.
Craige