The remote SMTP server is acting as an open mail relay. An open mail relay is an SMTP server configured in such a way that it allows anyone on the Internet to send e-mail through it, not just mail destined to or originating from known users. By processing mail that is neither for nor from a local user, an open relay makes it possible for an unscrupulous sender to route large volumes of spam. In effect, the owner of the server -- who is typically unaware of the problem -- donates network and computer resources to the sender's purpose.
You need to secure your mail system against third-party relay. Check references for details on fixing this problem.