> They measured a bigger gravitational effect on the particleNo, they didn't. They measured a phase shift in the particle's wave function. There is no "gravitational force" in free fall, and the particles were in free fall.
> gravity decreases with distance squared
The Newtonian gravitational force does, but the Newtonian gravitational force is irrelevant for an experiment conducted in free fall, as this one was. The gravitational potential is the key thing being measured, and it's not the potential due to the Earth, it's the potential due to a 1-kg "source mass".
> There is a big difference in being near the mass, as opposed to feeling the dimished effect of it from far.
The particles were near the 1-kg source mass.