[lostmsu]

This is only obvious when you yourself are not moving on a curved trajectory.

In GR curved trajectories lead to "weird" observations. For instance, I'd expect the side of the remote galaxy that is closer (visually, for you as an observer) to the center of your galaxy to be gravilensed slightly more than the other side. Because the effect is non-linear, it does not just compensate when sides are reversed.

P.S. Not claiming this has any significant effect on the described phenomenon, just that mirror symmetry does not apply.