In browsing through Astronomy Stack Exchange, I came across this question about orbiting the moon (Is it possible to achieve a stable "lunarstationary" orbit around the moon?). In further looking, I came across (Can I measure the moon's gravity?) which seems to indicate that with sensitive enough equipment, the moon's gravitational pull could be measured on earth. This prompted me to wonder if the moon's gravitational pull can be observed on the Space Station's or geosynchronous satellite's orbital path? And if so, if any compensation (either short-term or long-term) needs to be performed due to the moon's gravity. I would think it to be relatively inconsequential, but am not sure, hence the question.
According to NASA, satellites in Earth orbit don't experience strong enough interference from the Moon to "whisk a spacecraft out of the game". To a satellite in Earth orbit, the gravitational pull of the Sun is actually 160 times stronger than influence from the Moon. Source: A New Paradigm for Lunar Orbits
However, gravitational pull from the Sun, the Moon, planets such as Jupiter (as well as other factors such as solar radiation pressure, atmospheric drag, etc.) do cause enough interference to slightly alter the orbital path of any satellite orbiting Earth. To compensate for the deviations all satellites must periodically fire their thrusters for brief periods of time in order to maintain the correct desired orbit. If a satellite has no fuel to perform these "orbital stationkeeping" maneuvers it essentially becomes space junk. Source: Is the ISS, and all other satellites, affected by the gravitational pull of the moon?
And here is a reddit discussion: Does the moon's gravity significantly affect a satellite's orbit? where you can find an estimate of amount of force that the Moon exerts on a 500 kg satellite orbiting Earth at 23,000 miles to be ~2 Newtons.