Hi all,
To start with: at the same distance from the center of the neutron star (as long as you are outside the object), the gravitational field of a neutron star is not any stronger than that of its predecessor. At the surface: yes, but that's not what the donor star cares about.
The fact that it 'sucks' gas of its neighbor, is the neighbor's own fault. Because the other star evolves too, it grows. For the outskirts of the donor star, the gas is attracted about as much by its own star, as by the neutron star (or white dwarf, or black hole, a compact object anyway). Then it may be transferred to the neutron star.
This is easier to see, but the bias thing talked about above I think is a little bit overdoing it.