Without knowing the specifics of your equipment and software I can only draw on general networking principles and assume your programmer can talk beyond your local network, but here goes...

1. Check with the IT Dept to see that the port they opened is being forwarded to the TDE.
2. Verify that the IT Dept allowed TCP and/or UDP connections on the port as required.
3. Perhaps you can have thier IT department test the port and connection using tools like Putty or a port scanner to verify the port is truely open.
4. Perhaps your equipment is not set to allow the port from your programmer through your firewall. Check both TCP and UDP connections.
5. If possible, address the customer's network using thier IP number instead of a name to eliminate DNS issues on your side of things.

I hope you will find this helpful.