That is the slow speed #40 jet , you can still get a new one for $7.50 ------ soak that jet in some carb cleaner , then pick and blow at it some more
https://www.partzilla.com/catalog/honda/atv/1988/trx300-a-fourtrax-300/carburetor
https://www.partzilla.com/catalog/honda/atv/1988/trx300-a-fourtrax-300/carburetor