The mounting holes for typical LCD boards like this are usually 2.5 mm diameter (0.098 inch), so a #4-40 screw (0.114 inch diameter) as supplied in the kit is a poor choice. Drilling out the holes is probbly a good option, as long as the plated thru holes are not used as grounding connections.
I don't know much about electronics. I wondered what the hole size was and why the screws didn't fit. Are correct screws readily available? Using your numbers, the amount removed would have been about .0114 inch. Oh wait, it would be half that thickness all around, so .0057. Yep, I guess it might have removed the plating if there had been any. Anyway, seems to be working.
I used a 7/64" diameter drill to resize the holes. Worked perfectly :). Ensure that no copper shavings wind up in the circuitry.
I bought the 50A v4 deluxe kit. The screws were too tight to freely slip through the holes in the LCD board. I tried threading one through, which was sort of working, although it was very tight. I didn't like the force required. And I have a pet peave about fastener threads bridging. I like the top piece pinched to the lower by the screw head with no standoff due to intervening threads. So I got my drill index (64th inch increments) and tried the bits. The largest that went through freely was 3/32 if I remember correctly. The next size up (7/64, I think) would not slip through. I was a little nervous about it binding and cracking a corner of the board. But I chucked it into my battery drill, and it reamed the hole perfectly, with virtually no resistance ( or visible copper shavings), and then the screws fit perfectly. No slop, and no bridging.