My best measurements indicate the diameter of the screws are 76 mil and the thread pitch is 40TPI.
I've read from multiple sources that M2 by 6mm (metric) screws work well, as the fitting it is being threaded into is plastic, I'd imagine it is quite flexible. I've ordered stainless M2 screws myself to give it a go. Unfortunately I can't find anything that even resembles these screws from any standard.