Banners at the log-on time should be used to notify external users of any monitoring that is being conducted. A good banner will give you a better legal stand and also makes it obvious the user was warned about who should access the system and if it is an unauthorized user then he is fully aware of trespassing.
This is a tricky question, the keyword in the question is External user.
There are two possible answers based on how the question is presented, this question could either apply to internal users or ANY anonymous user. Internal users should always have a written agreement first, then logon banners serve as a constant reminder. Anonymous users, such as those logging into a web site, ftp server or even a mail server; their only notification system is the use of a logon banner.
References used for this question:
KRUTZ, Ronald L. & VINES, Russel D., The CISSP Prep Guide: Mastering the Ten Domains of Computer Security, 2001, John Wiley & Sons, Page 50. and Shon Harris, CISSP All-in-one, 5th edition, pg 873