There is a long, thin, rubber-y line wrapped around/connected to the water line pictured below.
Other angle:
The piece in question is loosely hanging via a zip tie on my main water line about shoulder height and can be moved up/down easily.
They send someone around every month to check the water meter? That’s crazy. Why would they do that?
I remember thinking the exact same thing, just the other way around, when I moved to the UK. I went from a country that measured what you used and billed you for it, to a country that just kinda went "oh, you're a family of 3? We'll charge you for... I dunno, like this much water? How's that sound?"