I didn't contact support, I had a lot of urgency with fixing this.
I looked around, and looked at the scripts, and I came up with just deleting the domain out of the /etc/localdomains file.
There does not appear to be any extra stuff to do to stop local delivery for a domain. I did find the /etc/exim.conf file shows you how the local_delivery lookup works. With our RH 7.3 and Cpanel install, it doesn't use a dbm file or anything, so I didn't have to do anything special. Just edit the file, and it works.
I next wanted to make sure the domain could relay through the server, so I found in the exim.conf file the relay file was called /etc/secondarymx
I added the domain to this file.
I don't have any experience with Exim, and I don't even know if that was necessary, but with Sendmail, you have to allow the domain to relay for the server to act as backup MX.
I only hope a click of a domain cleanup or add a new account in Cpanel doesn't undo what I've done. There doesn't appear to be any Cpanel or WHM scripts to address this situation.
Thanks for pointing me in the right direction.
Chuck