The idle mixture screw (American mechanic) and pilot screw (English mechanic) are one in the same. If yours has the little chrome plated "limiter" cap on it, the manual will tell you to break it off to remove the screw. A nice person on this forum (who shall remain nameless) gave me a technique for getting them out without breaking them off. Here it is;
The limiter is held on to the end of the screw with a dab of Loctite thread locker. If you heat the limiter cap with a soldering iron and simultaneously (and gently) pry it away from the carb, it will soften the Loctite and the cap will pop off. Under the cap will remain a nice little slot head for a mini screwdriver that you can use to adjust your idle or remove the screw.
If that doesn't work and the thing breaks off anyway, not to worry. I use a very sharp dental pick to stab into the flat, smooth head of what is left of the screw and turn them out.
Yes, it is a pain but it's what you have to do to get them out. The spring that is holding pressure on the barrel of the screw makes it difficult but if you use a sharp pick and contact the outer edge of the flathead, you can get it moving. When you think the screw threads are disengaged, it will still be hard to get out of the hole because of the O-ring seal being caught in there so using two picks to pry it upward and out will probably be necessary. A little shot of WD-40 can help get things moving. JUST MAKE DOUBLY SURE THE THREADS ARE BACKED ALL THE WAY OFF BEFORE PRYING! Several additional left turns after you THINK the threads are disengaged will ensure this.
You can then use a Dremel cutting wheel or your Xacto jewler's saw to put a slot in the flathead for a screwdriver. Or, you can go all original and put in a new screw set complete with new limiter cap.
Be advised that those "tiny tubes" can be a booger to get completely clean. And, the O-ring at the end is CRITICAL to the operation of the carb. I usually just replace them. Honda calls them a "jet set" and sells them with a new O-ring. Worth the money and will eliminate any doubt and confusion if you have additional carb issues. At the very least, do not reuse the old O-ring!
While you have them apart, pay particular attention to all the passages in the fuel bowl. I don't know if you have accelerator pumps on yours but if you do, they are also CRITICAL in the operation of the carb. Whatever the case, make real sure that any internal passages in the bottom of the fuel bowl are completely free and clear. Use the spray can straw to flush them out.
Once you have the idle screw out, prop the throttle plate wide open by wedging a mini screwdriver between the linkage arm and body. You will now be able to see all four fuel orifices in the throttle body. Use WD-40, brake clean or carb cleaner or all three to flush and back-flush those orifices. I usually start with WD and finish with carb spray. The straw is your friend! Use it to push up into that hole where the jet set (tiny tube) seats and spray your blues away! Cleaning that passage should have you seeing a pretty strong stream coming from the three orifices-two high speed-one intermediate-clustered in a triangle in the throttle body. You should get some from the idle orifice as well.
Flush the idle circuit by holding your finger over the idle orifice in the throttle body and injecting the straw into the hole that the mixture screw came out of. Then, hold your finger over the idle mixture screw hole and spray into the orifice. Takes a steady hand and dead aim. If you do this a couple of times you will get the hang of it. Having a couple of carburetors to practice on and compare will make you an expert Honda carb cleanin' man!
Ultra sound?? We don' need no stinkin' ultrasound!
Good luck.