LMC = diameter 6.24, therefore the no-go guage your'e using is correct (6.239/6.241).
The absolute size limits of the hole feature is diameter 6.24, so the gauge is telling you the hole is either line to line + or some size less than LMC. Based on the size of no-go guage you are using further investigation is required.
If you know what the mating size of the mating part and installation is going to be by statistical analysis, measured data or worst case analysis and that shows the installation is free and clear - accept it. Otherwise reject, rework or whatever is required. The good news is that you can remove material to to save the part.