the plastic piece is a limiter cap to allow a 1/4 turn mixture adjustment for high altitude usage. It will come off as OP stated, by prying with screwdriver, careful to not bend mixture screw. after removal turn screw in until gently seated, counting turns, so you may get adjustment correct after reinstalling...usually about 1-1/2 turns.
If your generator sat idle, without being run for extended period, more than 6 months, with bad gas in it, the carb. will probably have to be removed and completely disassembled and cleaned. There are lots of tiny passages that can plug up and make generator "surge". Also, common cause of surging on this model is Intake manifold developing vacuum leaks, causing lean mixture, especially at low loads.
btw, pic of carb posted by mudchucker is not from Emerald model, but later model HGJAB genset