Can't access your site. You appear to have maintenance mode on.
From what I can see from the theme's files, the code you need to remove is in home.php:
<span class="author vcard"><?php printf( __( 'By %s', 'erudite' ), erdt_get_author_posts_link() ) ?></span>
... unless you've modified the template files of course.
You may have to do some other modifications to make things look right after this has been removed, of course.
As usual, I'd recommend that you make changes like these in a Child Theme.
The code is a part of the loop, of course. Firebug can do a lot of things, but it can't tell you what's a part of the loop and what isn't. In fact, in WP, just about any output other than that in the header, sidebar and footer is almost by definition being output from the loop one way or another.