For best results, a full-bore sound moderator should always be removed for storage and not left on the rifle.
The reason is that an accumulation of toxic gases and chemicals can leach ¬ down into the barrel and etch away or corrode it when the rifle is in storage.
However, with a .22 rimfire, it is usual to leave it alone until there is a problem.
I would leave your old Parker- Hale moderator on after shooting, as .22 rimfires do not produce anything like the toxic concoction of acid and chemicals of a full-bore.
Also, if you continually remove and replace the moderator there is a risk that it will not be correctly tightened, and so would affect your zero.
As with all rimfires, I would give it special attention now and again: lubricate the screw threads and, more importantly, remove the build-up of crud, grease and unburnt powder that accumulates inside the moderator.
Clean it with methylated spirits, with the baffles in place to avoid disturbing the internals.
If this does not remove the debris from the baffle edges which might impede a bullet?s progress, then take it apart and give it a really good scrub.
When you reassemble, check the zero and adjust it if necessary.