This seems to have happened with the recent update to the Career Website builder tool. Content panels that existed before the update cannot be deleted. When editing a page you can click the bin icon, then click the "I understand. Delete..." confirmation button, then "Save & Publish", but if you then go back into the page to edit it, the content panel will still be there.

New content panels created after the recent update to the Career Website builder tool seem to delete with no problems, it's only a problem with content panels that existed before the update.