Please clarify - Are you removing the pilot jet from inside the float bowl, or are you trying to remove the airscrew on the outside of the carb? The airscrew adjusts air flow through the pilot system. Either way, be sure everything is very clean. Spray carb cleaner through those areas to try to loosen or remove deposits that may be interferring. I have not experienced any locked up jets and I have worked on some old and ignored machines. Remember lefty - loosey, righty - tighty. Make sure you have a good screwdriver tip, apply a lot of thrust force on the screwdriver, maybe put the carb in a vise and lean over it. The thrust force, into the screwdriver, shouldn't hurt anything, and it will help prevent the screwdriver from wrecking the slot in the jet or screw. If you still can't loosen it, try putting a small pliers or vise-grip on the screwdriver shaft. That should give you enough torque to remove it. Let us know how you make out.