Get yourself a nice stiff rake and rake as many of the stones out as possible. You don't want them in a lawn or planting bed. They're exposed now, it won't be hard. Throw a couple yards of dirt over it, and you're stuck with them forever.
There's nothing there that makes me think drainage would be an issue. There are healthy substantial bushes/plants nearby. If you want grass, most grass likes it on the wet side. My grandmother have a section of her property that was nearly swamp ( it was swamp until they dredged the pond) and I've never seen grass that lush anywhere else in my life.
