How to remove User login box from public event registration?
Actually this is a Drupal question. The login of CiviCRM is handled by the CMS. Form the screenshot I assume it is Drupal. So the visibility of the login block must be configured in Drupal.
You find the configuration with the following URL

http://&lt;servername&gt;/admin/structure/block/manage/user/login/configure


Here you can disable the login box for event pages in the following way: