You can probably update the firmware on the card, but there's no guarantee that a newer firmware would fix this (unless you know of a specific firmware you want to use). Tech Power-up has a collection of VGA Bios files which might have your card.
As was said before, though, be careful, and only do this if you know it will help you. This will void the warrantee, and it might brick your card (there's ways to recover, but it requires either reflashing the old bios before rebooting or having a second card to boot from).
Here's another option: Does your TV have any picture adjustments that can move the picture over a couple pixels (or a slight zoom, which wouldn't be as ideal) in order to hide the line? If it works, and your XBox still displays correctly, I'd give that a shot.