I've been pumping my cover water into my pool for the past 3 years.

I usually take my leaf net and clean all the big stuff off of the cover before pumping, and I don't pump all the water off the cover back under to the pool. The last bit of water on the cover is pretty murky.

When I do this, it does turn the pool water alittle funky looking, but usually within a day or two it is cleared up pretty good.