I don't think this is possible. I know you can set your media server to backup over a specific NIC, but not a remote agent.
If you had a second NIC in both servers, it's possible it could be done. You would do something like this:
1. NIC A on media server: 192.168.0.1 (main network card for normal LAN connectivity)
2. NIC B on media server: 192.168.1.1 (network card for backup VLAN)
3. NIC A on remote server: 192.168.0.2 (main network card for normal LAN connectivity)
4. NIC B on remote server: 192.168.1.2 (network card for backup VLAN)
You could target your backups over NIC B, and then either use the IP address of the remote server dedicated for backups, or add that in to the hosts file on your media server.