This may be because the caller might have originally send the email to the helpdesk in plain format (and not HTML format). Due to this, when Team Helpdesk add-in, for that matter, Outlook would inherits the format of the original email to any subsequent replies received or sent. Because of this behavior, you may experience that your signature and embedded images in the signature (if any) do not come out correctly in the subsequent emails.
If you want the signature/embedded images to show up, the workaround is to change the email format when replying to the email. You can switch the format to HTML format from Outlook (in your compose window easily). See below: