Code to stop Unable to Relay message for email

Hi
I have the code below, which works fine for sending internal email. Works on a PC.
But for external email, I get the message:
Mailbox unavailable. The server response was: 5.71. unable to relay
I've searched online, but the solutions seem to involve making changes on the exchange server. Is there a way I can add settings through code to fix this issue?

Dim smtp As New SmtpClient("mymailservername")
Dim mailClient As New MailMessage()

  With mailClient
            .From = New MailAddress(TM_FROM)
            .To.Add(stAgent_Email)
            .Subject = stSubject
            .Body = stBody
         End With

         'send the message
         smtp.Send(mailClient)

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