Before I try this thread chasing gimmick, ??

[gunwonk]

Have a couple of 8-40 scope base threads in a receiver that are slightly messy. Would like to clean them up.

As others have mentioned (assuming those are blind holes), you'll want a bottom tap, or "bottom" thread chaser.

Also known as cold-forming and fluteless taps

I've seen a few of those, but always as taper taps, never as a bottom tap.

If you don't want to make your own thread chaser, and don't want to remove any material, maybe a used, worn, and very dull 8-40 bottom tap would work? (Usual precautions, don't break it, etc.)

[Kenstone]

There are such things as thread FORMING taps, maybe not is this size, but I've used them before.
I think such a tap would work great for re-forming the threads without removing any material.

Think of it as internal "roll threading"...
jmo

[gunwonk]

Here it is, 8-40 thread swaging tap. Found on eB*y. (Where else?)

[country gent]

Also keeping mind with the "quick" fix of the screw threads, if it dosnt work then chances are it becomes a major repair. Drilling out a broken screw or worse drilling out larger and plugging then redrilling and tapping holes.