Just another quick snippet to add to the Grasmash Services archive.

This will allow you to POST an email address to /your_endpoint/user/password_reset and trigger a 'Forgot Password' email to be sent to the appropriate user.

<?php
/**
 * Implements hook_services_resources().
 */
function grasmash_services_resources() {
  $definition['user']['actions']['password_reset'] = array(
    'help' => 'Send forgot password email',
    'callback' => 'grasmash_user_password_reset',
    'access callback' => 'services_access_menu',
    'args' => array(
      array(
        'name' => 'email',
        'optional' => FALSE,
        'source' => 'data',
        'type' => 'string',
        'description' => 'The email address of the user whose password should be reset.',
      ),
    ),
  );

  return $definition;
}

/**
 * Send a password reset email for the specified user.
 */
function grasmash_user_password_reset($data) {
  global $language;

  $account = user_load_by_mail($data['email']);
  if (empty($account)) {
    return services_error(t('There is no user associated with email address @email.', array('@email' => $data['email'])), 404);
  }

  $vars = array('%name' => $account->name, '%email' => $account->mail);
  // Mail one time login URL and instructions using current language.
  $mail = _user_mail_notify('password_reset', $account, $language);
  if (!empty($mail)) {
    watchdog('grasmash', 'Password reset instructions mailed to %name at %email.', $vars);
  }
  else {
    watchdog('grasmash', 'There was an error re-sending password reset instructions mailed to %name at %email', $vars);
  }
  // Everything went right.
  return TRUE;
}
?>