Remove the extra headers from the e-mails sent
Apparently someone came up with code to put in a custom module that will remedy this issue:

http://drupal.org/node/461324

I've yet to try it though.

UPDATE:

I tried out an altered version and it worked for me. Here's what I had:

email_sender_override.info:

name = E-mail Sender Override
description = Overrides the 'Sender' of an e-mail message with the 'From' address.
core = 7.x
package = Webform


email_sender_override.module:

&lt;?php
/**
  * @file
  *
  * Mail altering function to override the 'Sender' of a mail message with the address
  * in the 'From' field.
  *
  */

/**
  * email_sender_override_mail_alter
  *
  * Alters the sender of the e-mail message to be the same as the 'From' address.
  * Taken from: http://drupal.org/node/461324
  * See also:   http://api.drupal.org/api/drupal/includes!mail.inc/function/drupal_mail/6#comment-3243
  *             http://drupal.org/node/656472
  *
  * @param message
  *    the full e-mail message being sent -- this will be altered
  */
function email_sender_override_mail_alter(&amp;$message)
{
    $message['headers']['Sender'] = $message['headers']['From'];
}
?&gt;