What you are referring to is the Jet Needle.
This is a needle shaped piece that fits inside the Throttle Slide (hollow, cylinder shape piece that the throttle cable is connected to.). When you turn the throttle on the right handle bar, this shortens the cable and causes the Throttle Slide to move up inside the carb. Inside the Throttle Slide is the Jet Needle; it is held inside the Throttle Slide by a Thrust Spring and a Disc (Washer). The tip of the Jet Needle fits down into the Main Jet. The Jet Needle also moves up as the Throttle Slide moves up. This regulates the amount of gas released up through the Main Jet from the float bowl.
The Throttle Needle has notches at the top and a Clamp Spring that slips onto the notches and can be moved up or down depending on the notch you put it on (normal is second notch from the top). This regulates the richness of the gas/air mixture. If you move the Clamp Spring down a notch it shortens how much the Throttle Needle protrudes into the Main Jet so when you twist the throttle the Jet Needle will be raised higher and allow more gas to come up through the Main Jet.
Raise the Clamp Spring on the Throttle Needle and you achieve the reverse result and less of the Throttle Needle is raised out of the Main Jet, thus less gas is released resulting in a leaner mixture.
I wouldn't recommend removing your air cleaner. You will suck more dirt and dust into your engine and eventually damage the cylinder and piston.
Puch made 3 levels of horse power engines to regulate the top end speed to conform to local or State speed limits for mopeds. They made 1, 1.5 and 2 HP engines. Puch regulated the HP through the size of the Carburetor Connecting Sleeve (Elbow shaped intake Pipe) 12mm intake for 1 and 1.5 or 14 mm for 2 HP. Puch used different Carburetors for the different HP models (see the new posting on carbs and jet sizes.) Not only were the main jet sizes different for the various carbs but also some of the other components like the Throttle Slide.
Also look at the white plastic flex tube on your Air Filter assembly. If the flex tube has black plastic inserts, pry this out at each end and put the flex tube back in the Air Filter assembly and put it back on the carb (preferably a 2 HP carb)
Puch made different exhausts for the various models but I doubt if you will find a new one that is not generic. Find a used one off a 2HP engine (Part number 3220.127.116.110.0 or 318.104.22.1680) and decarb and clean it.
So if you have a 1 or 1.5 HP and you want to boost it to a 2hp, you need to;
change the Carb Connecting Sleeve (Intake pipe) from a 12mm to a 14mm.
Put on a 2 HP carb, (see Puch carb reference table)
change the rear chain sprocket from a 40-tooth sprocket to a 45-tooth sprocket.
Change from a 99 roller driving chain (1, 1.5 HP) to a 98 roller chain 2 HP).
Do the Air Filter mod as described above
Put on a 2 HP Exhaust
Leave the Jet Needle valve on the second notch.
Make sure you have properly inflated tires
Make sure your wheel bearings (packed with axle grease) and chains are properly lubed.