Remove the theme info from main dashboard screen- not appearance

You can remove this via javascript. The class of the theme informations is versions and the ID of this Meta Box is dashboard_right_now.

The follow screenshot demonstrate how I find this class and id via Crome Webinspector.

    add_action( 'admin_footer-index.php', 'fb_remove_comments_areas' );
    function () {
        ?>
        <script type="text/javascript">
            //<![CDATA[
            jQuery(document).ready( function($) {
                $( '#dashboard_right_now .versions' ).remove();
            });
            //]]>
        </script>
        <?php
    }

For more hints to this topic see this plugin, that remove all comments functions and areas.

Also another hints. To remove menu or submenu items it is better, that you use the core functions remove_menu_page() and remove_submenu_page(). Also more information and examples in this post or via search on WPSE. The last one is to use a plugin, there have options for this, like “Adminimize” for reduce the admin area for different roles, not user.