The biggest problem I can see is that when you aim a laser pointer at something you generally miss somewhat. You can correct your aim because you can see where the beam is hitting. In this case that would be impossible.
Maybe if you carefully strapped your pointer(s) to a telescope…
No, this will not work. This is quite honestly one of the stupidest things I’ve ever seen. I little double-A powered laser pointer will not make a dot a quarter of a million miles away, going through the Earth’s atmosphere to boot, on the surface of the Moon.
Large observatories do shoot lasers at a reflector on the Moon left by an Apollo mission to measure the exact distance to it (within an inch). But their lasers are literally millions of times more powerful. So much so that they have to notify the FAA to keep aircraft away. It wouldn’t fry the plane like a ray-gun or anything, but it could temporarily blind the pilot (which would be bad).