I learned this the hard way years ago when both the pilot and main jets refused to move and I managed to damage them to the point of rendering that carb body into junk. Since I began using this simple technique I've never had another issue.
The most important thing is to have a screwdriver blade that fits properly—not loose and definitely not so tight that it won't bottom out in the groove--it must bottom in the groove. Search your screwdriver collection, or a multi-purpose screwdriver like the one pictured often has a blade to fit large and small jet sizes. Next, my technique is to fit the blade squarely in the groove, not tilted side-to-side or front-to-back, really grab the handle, push down hard onto the jet, then give a quick and forceful "snap" to break the jet loose. You may only have one or two chances to get it right, so take your time to be square in the jet's groove.
If a jet still refuses to budge, rather than force it to the point of breaking, I will soak the threads in parts penetrant overnight and then add heat from a small butane torch and try again. If you're in the unfortunate circumstance of having a broken jet, you can try to cut a new screwdriver groove with a Dremel tool or grab with a small vise grip or, as a last resort, carefully drill out the jet with successively larger bits until the remaining threads (hopefully) twist free.


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