Even if a black hole missed the Earth, just flying through the Solar System would be enough to completely disrupt all planetary orbits.
Any mitigation strategy to alter the course of the black hole itself would require so much mass/energy to the point that we'd be making our own black holes for the purpose of space travel, so the Solar System wouldn't matter too much in the grand scheme of things anyway.
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But as we look at smaller and smaller black holes outside known mass ranges (e.g. primordial black holes, artificial black holes, etc...), things start to change.
A black hole with the mass of anywhere smaller than a star to the mass of a planet is more or less still going to result in the same effects as a stellar mass black hole.
A dwarf planet mass black hole on a collision course with Earth would destroy Earth. If we knew it was coming say a 400-1000 years in advance, we may be able to accelerate a large asteroid into it resulting in a different trajectory for the black hole causing it to miss the Earth, but the tidal forces would still rip the Earth apart or at least send it into a different orbit.
An asteroid mass black hole would strike the Earth causing a massive amount of gamma radiation cooking everything on the surface as it entered the Earth's atmosphere only for it to continue through the planet, emerging on the other side with another bout of radiation cooking before continuing off to shoot back out into space. It would be about the same as two small moons crashing on either side of the Earth.
A tennis ball mass black hole going close to the speed of light would go right through the Earth without too much fuss. The black hole's radius would be too small (smaller than an electron) to cause any damage.
Edit: Added "going close to the speed of light" to the tennis ball mass black hole explanation. If it was not going fast to the speed of light, the black hole would evaporate before it could travel through the Earth. The evaporation would probably also cause so much heat it would cook the planet.