Question

imagine that a new planet is discovered with two moons of equal mass, moon A and moon B. The mass of the new planet is greater than the combined mass of its moons. Moon A is farther away from the new planet than moon B. What is the planets gravitational pull on moon A compared to the gravitational pull on moon B

Answer 1

The gravitational pull on moon A will be lower since it is further away from the new planet.

Answer 2

When two objects are farther apart, the gravitational attraction
between them is weaker.

This is a big part of the reason why we are more strongly attracted
to the Earth than we are to Jupiter or to the Sun.