Modern Buddy

I recently bashed my exhaust pipe into a curb while turning and as result had to replace the exhaust. Upon removal of the old exhaust, I noticed that the owner before me had cut off and plugged the little pipe that feeds off of the main exhaust (see pic). Additionally, he had also removed the air filter in the black cylinder (thing that connects to the hose in the pic).

Probably a stupid question, but does anyone know what impact that modification has on the scooter/if it is bad for it in the long term? I know since replacing the busted/modified exhaust with another stock exhaust, it accelerates very sluggishly, however, has a higher/smoother top speed.

I'm currently either going to replicate the prior mod, or possibly trying re-jetting the carb to see if i can improve starting acceleration. Any thoughts would be much appreciated.

Apologies if this has been covered before, however, i searched for 20 minutes and couldn't find anything.

That mod was to bypass a power robbing emission system. Your Buddy must be newer as I know the Zuma's got the emission canister added in 08 onward. Im not sure on a Buddy as to what needs to be done, have never seen a newer 50cc Buddy. You can find a used O.E.M. exhaust on buy the new "performance" stock replacement OR start tuning with a expansion type exhaust. Im sure someone on here knows the correct way to be sure that emission system is bypassed correctly, as that could be a root cause to your acceleration issues.

Depending what exhaust you got to replace the damaged one you may need to do some roller tuning in the variator. Lighter gets better take off/heavier more top speed. Its a balance act to get it correct but the Buddy is very easy to work on, so dont let the tuning idea scare you. Lots of people go with sliders (Dr. Pulley's) here and can give you a good idea of what weight to start with.