First of all we have to know that the satellites which are their own orbits are nearer to moon or earth and which is the greater in mass. Is that Earth or is that moon?
So the answer is the satellites which are removing around the definite orbit are much much nearer to earth only not to the moon. And the mass of earth is much much greater than the moon, so the gravitational force to the satellites because of the earth is multiple times the gravitational force due to the moon. So th satellites which are nearer to the Earth are removed by the gravitational force due to the Earth only.
(the main thing you have to remember that all these type of attraction due tho gravitation of various planets depended their relative position about any object and the relative masses compare to them)