Query String and hook_page_alter()
I'm not sure why you'd need to get it from the $page variable, you can get the query string from the $_SERVER superglobal at any point in the page execution, and convert it into an array with PHP's parse_str():

function MYMODULE_page_alter(&amp;$page) {
  // Convert the query string to an associative array named $qs
  parse_str($_SERVER['QUERY_STRING'], $qs);

  // For the string name=jeff&amp;foo=bar:
  //
  // $qs['name'] = 'jeff';
  // $qs['foo'] = 'bar';
}