True, there would be some signal loss, but the signal could be sizable since there would be a “ring” of returned radio transmissions that could be received from the black hole…not sure how it would compare with a mirror though.
Depending on the signal’s trajectory and distance from the BH, the signal stream could be redirected in any direction (including 180 degrees) or be pulled in by the BH and never escape. Still have no idea on how weak the return signal would be, but distance traveled would be a factor.
Should our physicists crack the going faster than the speed of light conundrum, there will still be an engineering problem with respect to the size of telescope you need to discern any detail on the surface of the earth. Rayleigh’s Criterion can tell us the minimum aperture a telescope will need. I just did a bit of maths and in order to distinguish between two objects 1m apart at a distance of 100 light years your telescope is going to need a mirror with a diameter of 649 million km. So when you put in your budget request for the Kobayashi Quantum Time Flux Project, you best factor in an element for mirrors, unfeasibly large variety.
Well you could always use optical interferometry to produce an effective aperture of that size. If you can evade C, then throwing up a number of station keeping telescopes seems like a manageable feat.