One likely major obstacle is that if their network admins have any clue whatsoever, your traffic is being blocked at their perimeter by a firewall. If not, their database is likely compromised anyway.

That said, why on Earth would you want to even consider connecting with plaintext to a customer database over the internet? Has anyone in your legal department (or theirs) reviewed the content for potential regulatory problems?

Get your network team talking to theirs about some method of an encrypted communications tunnel between these two servers. If you don't need the data in real time, you could also exchange it as an encrypted file.