When you add a header image to the Pearsonified Skin under Thesis Admin → Skin → Header Image, the image is not linked back to the home page of your site by default. That’s because in this Skin, the Logo Image is meant to serve this purpose.
However, if you don’t plan to use a Logo image, you may want the Header Image to serve as the link instead. To make that happen, add the following code to the custom.php file (which is located in the /wp-content/thesis/skins/pearsonified folder):
add_filter('thesis_pearsonified_link_header_image', '__return_true');