TMEC issue i believe

[Hooligan]

Hey guys, having a slight issue with my TMEC 200. Ill be attaching photos of whats going on because ive no clue what the name of the part is.
There is a small metal tube on the right side of my cylinder that leads over to the left side to what looks similar to a mini carburetor, the original hose blew a hole in the side which caused the bike to sound much deeper and gives a crackle on the deceleration. But nothing else went wrong, all seems fine but i sure dont believe that tube would be there just for the heck of it.
So i went to a local hardware store, bought fuel line that was nice and thick and seemed good quality and replaced it, and barely a day later the same thing happened again.
Now i understand i probably just need better tubing that is more suited for such heat, but im really curious as to what that thing even does and if its worth my time. Any help would be greatly appreciated. thanks