GL-MT3000 server --> GL-MT3000 client <--not using the server DNS

I work for a giant tech company, 100% remote, but they have this stupid rule of not letting us move. Anyways, I just got a hold of 2 MT3000 routers and I set one up at home, wired to my home fiber modem, and the other as a client router. They connected successfully via Wireguard and it's very speedy. I tried it at a friend's house and it connected with my house IP perfectly.

The problem is, comparing results from at home versus connected via the client router shows different DNS addresses and servers being used. Should I worry about this once I travel abroad for a few weeks? (I will be connecting via Ethernet to my router abroad and physically disconnected the WiFi antenna cable inside the work laptop. I also disabled it via software, but I went the hardware way just to be 100% sure they won't remotely turn on my WiFi to triangulate my location.)

If this DNS difference poses a risk, how do I set it to use the same DNS servers as the ones I use at home? Or how can I configure the server to forward this to my client router abroad?"

Let me know if you need further clarification or assistance!

If this DNS difference is a risk, how do I set this to use the same DNS servers as the ones I use home? or to get the server to foward this to my client router abroad?

Can you check your wireguard config and change the dns?

Just tried that and it didnt work, it gave errors and couldnt browse anything

Can you give the screenshots of the test.