No, you don't.
Perfect Moose Greg is connected to the boiler of your espresso machine. Under the counter, your espressomachine uses water that has first gone through a filter. Since Perfect Moose Greg uses the filtered water coming from the espresso machine, no separate filter is needed.
Grinder | Espresso machine | Shut off Tap | Pressure regulator | Boiler | Perfect Moose | Rinser | Filter