I had the same issue, but with the throttle and the choke at the same time, I ended up removing the carb with the cables attached, so loosen it from the handle side, it is way easier to do it this way and do an accurate adjustment before installing again as well.
1983 Honda ATC250R
1983 Honda ATC200E BIG RED (sold)
1984 Honda ATC200E BIG RED
1984 Honda ATC200X (sold)
1985 Honda ATC70 x 3
1985 Honda ATC250ES BIG RED
1988 Honda ATC250ES BIG RED
1995 Honda Frankentrike 50cc 2-stroke
2001 Honda TRX90
2004 Honda TRX300EX (sold)
2008 Honda TRX250TM
1976 Suzuki RV90M (sold)
1967 Vespa Primavera 125
1958 Massey Ferguson 35