The reason the bike no longer backfires....is there is nothing to limit the flow of fuel other then the size of the hole...and your bike is running too rich. You fuel mileage is going to be low.
You should get a replacement screw, then it if requires you to open up the mixture screw more than 3 turns to get the idle mixture correct, you should bump up the size of the pilot jet. (It is a fuel screw on this carb....not an air screw).
This is the proper way to adjust your idle fuel screw. Pay attention to the explanation of how to size the Pilot Jet. If the best mixture (speed) is obtained less than 1 turn out - you need a smaller pilot jet. If your best mixture (speed) is obtained at more than 3 turns...you need a larger pilot jet.
https://www.youtube.com/watch?v=zm5mB3R8Ucw