I’m 99% sure that these screws are 5 BA, which is of course in engineering terms, a “non-preferred” thread, like all the BA odd numbers. I have just rebuilt six Pilgrim pumps and have had to reclaim the existing slightly mangled screw heads by careful work with Swiss files. They can then be treated with “gun blue” compound to restore the nice original finish. (All the ones that I have are not electroplated nickel or chrome, nor are they blacked. They are definitely a gun blue chemical finish) One or two were mangled beyond redemption but I was able to find replacements off a pump that couldn’t be rebuilt as the body was partly ground away from a trip along the road surface at some time! It yielded good plungers and drive worm too.