You would use that insert to retain the original square O-ring used on that regulator stem.
It's not used with the much thicker nylon gasket, which is fine...
I've never seen a square o-ring.
Anyway, it seemed to fit nicely between the regulator output and the hose barb adapter so I put it there. Seems to work.
Looks like the retainer for the flat washer, however the washer you have looks old and stretched out. Check out this video for changing the flat washer on a TapRite regulator.