If you are using email archiving (Admin->Configuration->Email Options->Email Archiving Active?)
and you do not want to archive your SMS message emails, edit the file

includes/classes/observers/class.msg_owner.php

and change "msg_owner" in the call to zen_mail to "no_archive", i.e.

zen_mail('Shop Owner', $this->owner_phone, $email_title, $email_text, STORE_NAME, EMAIL_FROM, $empty_block, "no_archive",'');

Scott