The carburetor throttle opener is used to increase the idle when the bike is in gear, but allow the idle speed to be the same when it's in neutral. The solenoid controls vacuum to a diaphragm connected to the carb. The solenoid receives it's signal from the changing relay. The green/black wire should connect to that relay. The the 77/78 model also uses a speed warning unit in line to turn off the system when the bike is decelerating at speed.
Without the system working properly, the idle can be adjusted to the proper speed in neutral, but may be too low when in gear, or visa versa. A happy medium sometimes can be found, but when working properly, the bike idles very nicely in both modes.
A filter on the end of the breather hose will work fine, and to some people, it's the preferred method.
.....Paul