Of course General Relativity is not the final answer, we know that. But that does not mean we know nothing about gravity, or that we somehow can't use our current theory to make predictions.
Dark matter as a concept assumes General Relativity is good enough, and takes it as-is. Without modifying gravity we need some other way to explain the discrepancies like galactic rotation curves, and so for dark matter we add in some new, so-far unseen, particles. We also know they have to interact very weakly with normal matter besides gravity, otherwise we'd would already have noticed them in existing observations and experiments. Based on this we can make predictions.
What would happen if we have some matter that only interacts gravitationally buzzing around?
Well as mentioned in my previous post such matter can't cool down and clump like normal matter, so instead it would be spread out in diffuse blobs around galaxies. And when we model galaxies with such dark matter halos we find that indeed, that might explain galaxy rotation curves. It also makes other predictions which also seem to match other observations. So overall dark matter looks like a pretty good candidate.
The alternative of course is to assume there aren't dark matter particles, but rather that GR has to be replaced or modified in some non-trivial way. There are many people working on that.
However they're so far struggling, because it turns out to be very difficult to change or replace GR without failing to match existing observations. So that seems to indicate that GR is a pretty darn good theory of gravity.