Recirculation pump is quiet, but the pipes knock when it stops

A recirculation pump can run quietly and still be associated with knocking or a brief change in hot-water movement when it shuts off. What observations help distinguish check-valve chatter from water hammer or vibration in the piping, without taking the pump or valve apart?

Would it help to note whether the noise happens at startup or shutdown, and whether a faucet is being opened at the same time? I’d also expect the control type to matter: a timer-controlled pump may stop on a schedule, while a demand-controlled one may stop after a call for hot water. Is there a reliable way to narrow down the source from those patterns, or is inspection by a plumber the sensible next step before changing the system?