I moved into a house in northern Virginia and came across this device on the shower head in the master bath. It's about 4 inches across, maybe 3 inches deep. It has a dial that can turn and displays the name of a month in a little window.
There aren't similar devices in the other bathrooms. It does not seem to be part of the shower head itself because of the different finishes.
The only thing that comes to my mind is a filter, probably activated charcoal, to remove residual chlorine. I doubt that it is necessary with the normal public water system. One sets the month when a new filter is installed as a reminder to change on some schedule.
Such a filter must be changed on some schedule because over time a biofilm will build up on the filter cartridge.
Edit
The original poster located this unit https://www.homedepot.com/p/Sprite-Showers-Universal-Shower-Filter-in-Chrome-SL2-CM-R/202386562
It's likely a copper media filter for chlorine only, not a particulate filter. I believe copper alters chlorine to something less smelly and drying. Occasionally shake it to keep it working.
