We call them anti-siphon valves. More typically, they are found on landscape valves to prevent yard water from siphoning back into the house supply. They are required by code for that purpose. Otherwise, our exterior hose bibs do not require an anti-siphon valve -- but you area might have a different code.
It is usually best to assume that if you have such a valve, it IS required by local code. Keep it and work around it.
You are "re-fitting" what? Changing the hose bib? Just shut off the main and change out the bib, leaving the valve in place. Changing the water heater? Leave the valve and change out the connection to the heater.