Green thingy is the coupler, its a plastic/rubber/compound piece that takes the torque from the motor so its not metal on metal. Simple fix vs replacing the gears or the shaft in the snout. 3 holes for the gear, the other 3 are for the shaft in the snout. It is the middleman that takes all the abuse every-time you start, stop, WOT, or just goose the engine.
What happens is the tight fitting holes wallow out and become egg shaped and it causes slack, and while idling the slack causes a rattle. When your on the throttle it goes away, but back at idle, slacks up and wobble wobble wobble wobble.