Seems that there is one hook for login_footer, but that there is no real action that ads the footer link leading back to the home page. I found the code here on line 133 of wp-login.php:
function login_footer($input_id = '') {
?>
<p id="backtoblog"><a href="<?php bloginfo('url'); ?>/" title="<?php esc_attr_e('Are you lost?') ?>"><?php printf(__('← Back to %s'), get_bloginfo('title', 'display' )); ?></a></p>
</div>
<?php if ( !empty($input_id) ) : ?>
<script type="text/javascript">
try{document.getElementById('<?php echo $input_id; ?>').focus();}catch(e){}
if(typeof wpOnload=='function')wpOnload();
</script>
<?php endif; ?>
<?php do_action('login_footer'); ?>
Main snippet I do not want to load and will probably hide with CSS as I do not see another way is:
<p id="backtoblog"><a>/" title="<?php esc_attr_e('Are you lost?') ?>"><?php printf(__('← Back to %s'), get_bloginfo('title', 'display' )); ?></a></p>