Hello Joanna,
Thanks for writing in!
The banner header is actually a slider that came from the Training page that appears in the search result’s page. This is a confirmed bug that has been fixed already in the recent release. After further investigation, I found out that you are using an older version (X 6.4.6) which is why this banner bug is displaying in your site. Please be advised that we have released X 7.1.2 and Cornerstone 4.1.2. It is now available in automatic updates. You can now update to this latest version. This latest release contains fixes for several issues so be sure to check out the changelog (http://theme.co/changelog/).
After doing the updates, always remember to clear all caches (if you are using WP Rocket, WP SuperCache or W3 Total Cache) when updating so that the code from the latest release is always in use. This will help you to avoid any potential errors.
With X theme, adding custom banner or header to archive and search pages will only be possible with custom development which is beyond the scope of our support.
Hope this helps. Thank you for your understanding.