Yeah, they used something like fluctuations in the WiFi signal, so you can turn it off. I suppose they could broadcast secretly without an SSID, but there are apps that will show it, so I doubt they would.

They can also see more than just movement: https://www.popularmechanics.com/technology/security/a42575068/scientists-use-wifi-to-see-through-walls/

Ask for just a plain modem and buy your own WiFi router. If that isn’t an option, disable the routing functions and turn off the WiFi and buy your own router.