The MX record change you need to make is in the Control Panel for the registrar that hosts their DNS records. You don't set it internally on your server.
What you are querying when you do an NSLOOKUP is the DNS that is recorded on the registrars DNS servers. Change the IP associated with the MX record on the registrar's site and the mail flow will change to the client.
This will take about 24-48 hours to propogate around the world, so don't expect an immediate response.