Listening to non-verbose log entries only with enterprise library

I'm marking verbose log entries like this:

Logger.Write(new LogEntry 
{ 
    Message = "Using debug quote id...", 
    Severity = TraceEventType.Verbose 
});

How do I configure enterprise library event listener to log non-verbose events only

You need to set your trace switch to only listen for Warning or Error level events. You can do this in your application .config file.

Check out this article or this one from MSDN.