The benefit of filtering a detector output

The signal on the headset with no filter.

Adding the choke cleans it up a bit but still some there

Adding the capacitor to provide an RF bypass to ground produces a clean audio.

Alternately you could bypass the head phone BUT the RF would still be in the phone leads. Better to remove it before the choke.

The capacitor is before the choke in this circuit.

I would suggest trying a bypass cap too.