gravity - How can one interaction influence the way another interaction generates mass?

This question arose as a follow-up of this one and applies generally to all interactions and all ways to generate mass.

To make it clear, I take here the example of the neutron, whose mass is in most part generated by the strong interaction (see this post), and the neutron star, inside which neutrons have a large gravitational binding energy (see this post).

When the neutron binds gravitationally to the neutron star, it loses a significant fraction of its mass. However most of the mass comes from the confining field of the strong force. I would naively expect that the strong interaction would behave the same way regardless if we are at the surface of a neutron star or at the surface of the Earth. Inside the neutron star, the high pressure has an effect of putting the quarks closer together and decreasing the neutron mass, but this is a separate effect (we can see that if we consider the case where the neutron is just outside the surface of the neutron star as compared with a long distance away -- the closer the neutron, the lower the neutron mass solely due to the gravitational potential). So how can the gravitational interaction influence the way the strong interaction generates the mass?