If you look at the source:

40          <p id="footer-upgrade" class="alignright">
41                  <?php
42                  /**
43                   * Filter the version/update text displayed in the admin footer.
44                   *
45                   * WordPress prints the current version and update information,
46                   * using core_update_footer() at priority 10.
47                   *
48                   * @since 2.3.0
49                   *
50                   * @see core_update_footer()
51                   *
52                   * @param string $content The content that will be printed.
53                   */
54                  echo apply_filters( \'update_footer\', \'\' );
55                  ?>
56          </p>
57          <div class="clear"></div>
58  </div>

像这样的东西应该可以满足您的需要：

function test_update_footer_wpse_206382() {
  return \'|| Hello World\';
}
add_filter( \'update_footer\', \'test_update_footer_wpse_206382\' );