Tesla expects it to be connected so they can get data from (and theoretically push firmware to / support) the inverter. If you have a solar only install, the data coming from there is what is pushed through the tesla app, is my understanding. If you (like you and I) have powerwalls, the TEG gathers all that data, so the solar gateway (little black box) function is for support of the inverter.
I dont know what (if anything) teslas contract says about connecting that device, but the TL ; DR version is, tesla uses it to support the inverter (supposedly) so they expect it to be connected. If you dont connect it, you wont lose any data access in the tesla app because you have powerwalls. They will likely keep nagging you about it (might even call you) though.
I have mine connected, FWIW, and I have an old inverter they no longer sell.