PHP List is one of my favorite newsletter applications, and it was a great effort and dedication by the developers to code it. You can remove the Powered By notice at bottom of emails by commenting near line 139 in /admin/connect.php where you can modify the HTML for the footer text and image for PHPList. However, be sure to read the author’s comments before modifying this code. PHPList is a great application and you may only change this footer if you have a real need to do that. It should be great if you can leave this so many people know about this PHPList project team instead of other commercial solutions like Constant Contact or Mailchimp.
If you want to effectively remove the image from the bottom of HTML emails, then you can open /admin/sendemaillib.php and look at line 121 where it says signature. Replace that value with \n\n\n\n.