This is due to your ISP blocking external access to their SMTP (sending) email server. This means that unless your computer is connected to their network, they will not allow you to send using their outgoing (SMTP) server. ISPs implement this to reduce the risk of their servers being used for spam. They notify you by sending you that strange 'relay' email. Some ISPs support SMTP authentication which basically makes you log in (proving that you are who you say you are) before you send the email.

Not all ISPs support this feature, so we have set up its own SMTP server for customers using Mobile Connect - smtp2.vodafone.net.nz.

If you change your outgoing mail server to smtp2.vodafone.net.nz then you should be able to send.