Drupal: Edit email template from contact form

When submitting a message in my site-wide contact form in Drupal 6.x I get the following message along the top of every message:

[Name] sent a message using the contact form at [www.mysite.com/contact]

I would like to remove this message. Looking around, I've found it comes from the contact.module here:

$message['body'][] = t("!name sent a message using the contact form at !form.", array('!name' => $params['name'], '!form' => url($_GET['q'], array('absolute' => TRUE, 'language' => $language))), $language->language);

I've done a bit of research and it seems that I need to create a custom module with a hook_mail_alter() function to edit the contact.module. When it comes to this I get a bit lost. Could anyone kindly take me through the steps to accomplish the task?

Many thanks.

I did something like that recently. Here is a template you can use to get what you need. Most is from the contact module. The code below is from Drupal 7 but should work as is in Drupal 6.

/**
 * Implementation of hook_mail_alter().
 */
function modulename_mail_alter(&$message) {
  if ($message['id'] == 'contact_page_mail') {
    $language = $message['language'];
    $params = $message['params'];
    $variables = array(
      '!form-url' => url($_GET['q'], array('absolute' => TRUE, 'language' => $language)),
      '!sender-name' => format_username($params['sender']),
      '!sender-url' => $params['sender']->uid ? url('user/' . $params['sender']->uid, array('absolute' => TRUE, 'language' => $language)) : $params['sender']->mail,
    );
    $message['body'] = array();
    $message['body'][] = t("Your custom message with variables", $variables, array('langcode' => $language->language));
    $message['body'][] = $params['message']; // Append the user's message/
  }
}