It's in _feedback.php, to make sure you're in the right file. I'll help later if you haven't worked it out before then.

Ok, here's what you need to do.

Crack open _feedback.php

Find

<cite>
				<?php 
				$Comment->author();
				$Comment->author_url( '', ' @ ', '' );
				?>
				</cite> says: <br />

And replace it with this:

<cite>
<a href="<?php $Comment->author_url( '', '', '', false ); ?>"><?php $Comment->author(); ?></a>
</cite> says: <br />

This will still say [visitor] at the end, since removing that requires hacking core files. It can be done, but will need to be done again after each upgrade. This will survive (most) upgrades.

Thanks, worked perfectly!

why is it that with this neat little trick, a visitor who does not add their own URL is provided with the sites URL by default?

That's exactly why I didn't put that in with my modified version of the comments.