WordPress finding a specific link to edit it

I was handed down a website to edit with wordpress and I no basically nothing about wordpress.

I am trying to edit a link in the front page of my website however I just can’t find this link. I have looked through the every page’s PHP (You can look through the PHPs of your site in HTML per page in wordpress) and I just can’t seem to find it.

It isn’t in the Header.php or the footer.php or even the archive.php I’ve looked everywhere. It is basically just a link in the middle of the front page that I can’t seem to pinpoint (See image, link is in the red circle).

Please help me, is there a quick way to find this link? Or do you know where this link would be placed in the wordpress dashboard editor?

UPDATE 12/06/14

I found this code in the Frontpage.PHP

<?php`enter code here`
                    foreach ($query as $post) {
                        setup_postdata($post);

                        printf('<div>');
                        printf('<div class="box">');
                        printf('<h4>%s</h4>', $post->post_title);

                        printf('<img src="%s" />', wp_get_attachment_image_src(get_post_thumbnail_id(get_the_id()), 'full')[0]);

                        printf('<p>%s</p>', get_the_excerpt($post->ID));
                        printf('<a href="%s" class="button">Read more</a>', post_permalink($post->ID));
                        printf('</div>');
                        printf('</div>');
                    }

                    wp_reset_postdata();
                ?>

Think this is where I have to insert the link I want it to lead to?