Looks like that whistle part is an insert into the lever body. I'm guessing the only fix would be to dismantle and put (drill) out that insert and have a new one machined. Fat chance of that ever happening.
In other (bad) news, I picked up an Empire Model 50 pump and it also came in yesterday. The brass rod for the "bucket" had come loose and there was a badly rusted ball bearing (about the size of a BB) - I assume it acts like a check valve. I cleaned up the ball with 1500 wet sandpaper, figured out a bucket to / leaver rod, and generally cleaned up the insides of the pump/bucket. Movement is nice and smooth now but it will hardly pump water. I can't figure out why, perhaps it is just too worn too suck up water. The funny thing is, my Empire Windmill's pump looks like a 100 year old rusted junk car inside the pump but it can move water like crazy with very little action movement.