A very interesting idea!
Although I don't think that the black hole cared much of those few photons from earth.
Expanding it, how long until my hand waving could cause a strong enough "butterfly effect" for an observable cosmic phenomenon to occur beyond our solar system?
A million years? 100 million?
Edit: Thank you for your comment. Just keep it! Sometimes people here are just a bit quick to judge. It's amazing to think humans could have affected such a monster at all, no matter how little. Even for a handful of photons worth.