Besides the 3mm allen key, you'll need some way of checking the idle mixture. The accepted way to do this is with an exhaust gas analyzer or sniffer. On vehicles without a feedback system such as an oxygen sensor (and maybe also for carburated engines only), there's a device made by Colortune(?) that lets you view the color of the combustion flame. It didn't seem more accurate than winging it, but it has high entertainment value
Turn the idle mixture screw a quarter turn one way, let it stabilize for a couple of minutes and check for improvement. Then turn it a quarter turn the other way and check again. It takes a while for the system to equalize at the new setting. If an adjustment either way doesn't yield an improvement, your problem is probably something other than a misadjusted idle mixture.
FWIW, my guess is that whoever tampered with the mixture screw was trying to sort out the idle fluctuations.
BTW, I think the plate is reacting to the situation, not causing it. Or maybe I misunderstood that statement.