Wireshark is a program that monitors network packets traveling across a network. It's free and popular. The definitive way to answer this question would be get Wireshark, take a day to learn it, and apply it.
The filter to see traffic from the source site would be:
(ip.src == [ip address of source]) && (ip.dst == [ip address of target])
Swap ip.src and ip.dst to see what's coming back. You could actually combine both in one filter expression actually.
This would work provided that you're on the network through which the packets are traveling.
One final item: Here's a description of PKI (https/SSL/TLS): http://www.mitre.org/news/the_edge/february_01/steve.html
I Wiresharked a sort of similar situation, and verified I was sending and receiving TLS (https) traffic. But it wasn't this situation exactly so I don't want to speculate.