Hi,
As I see myself doing that I have two options:
1st
Configure my router to the same subnet your device is using (in this scenario 172.31.205.x) and then access the device and change the static IP address into something more comfortable for me. If your device somehow has a static IP address set it means there is a way to change it, maybe somewhere in the internal configurations between config files?
2nd
Setting up two routers, which have two different IP subnet ranges. Router A (which is connected to your PC) to have 192.168.1.1, and Router B which will connect your unknown device with subnet 172.31.205.x. So let's say Router B is 172.31.205.1.
I would connect Router A LAN to Router B WAN and set static routes between them.
Router A would have a static route to 172.31.205.0 with MASK 255.255.255.0 and gateway 192.168.1.x (whatever Router A DHCP server gave to Router B).
And then I would allow the traffic between them with these commands:
Router B:
iptables -I FORWARD -s 192.168.1.0/24 -j ACCEPT
After all of that, you should be able to ping each one of the sides and reach them.
In your place, I would be more interested in going after the first option as you might find configurations that could lead you to easier set-ups.
EB.