Every paint color reflects a unique bundle of wavelengths. Technically it's called a spectral reflectance curve. Or, you could call it a color's fingerprint to make it easier to remember.

The light in a room is comprised of a unique bundle of wavelengths too except these wavelengths beam and bounce all around looking for something to reflect off of - like a painted wall.

When you see color, what you see are the parts from both bundles that align and partner up. That special alignment of wavelengths creates the atmosphere in a room for you and your eyeballs to experience.

Most of the time people don't notice specific color qualities of the inherent light in a space.

You, however, already know/feel that the inherent light leans green.

The answer is choose a gray that does not have the same characteristic of green. Stay away from grays that belong to the green-yellow or green hue families.

Choose a gray from some other hue family to reduce the odds of it having some degree of greeness with which to respond to, and align with, the inherent, green cast light. Some Sherwin Williams' grays to check out and compare:

7022 ALPACA
7023 REQUISITE GRAY
7024 FUNCTIONAL GRAY
7025 BACKDROP
7026 GRIFFIN
7031 MEGA GREIGE
7072 ONLINE
7073 NETWORK GRAY
7078 MINUTE MAUVE
7079 PONDER
7080 QUEST GRAY
7081 SENSUOUS GRAY
7670 Gray Shingle