Looks like some app on her computer is trying to connect to nonexistent domains. It wouldn't be an issue if the modem wasn't buggy.
Option 1.
Set the DNS server in her computer's IPV4 settings to something else than the modem's IP.
Use the ISP's DNS server IP, or Cloudflare's free DNS (1.1.1.1), or Google's free DNS (8.8.8.8 and 8.8.4.4).
Option 2.
Manually add the bad domains to your OS to resolve as a local IP (127.0.0.1).
You can do it in the hosts file. If it's Windows, this one explains how to do it:
https://www.thewindowsclub.com/hosts-file-in-windows
Option 3.
Block those domains in the computer's firewall.
Option 4.
Disabling modem log could be a solution too as suggested above.