The black holes distort the image of distant galaxies as the light passes through them.
I assume you mean it distorts the image of distant galaxies as the light passes around them. If the light of a distant galaxy passes through a black hole, we won't see it. If the light simply comes close to a black hole, its direction will change.
We can actually see interstellar objects behind black holes due to this phenomenom.
You're right. Right wording would be "around" instead of "through". I edited that part.