Not sure what it is but many fungi feed on dead wood/organic matter, so any dead stumps, wood chips, manure.
They rarely affect live growing plants.

The mushroom/toadstool is the fruiting body that will release more spores [seeds]. So you could remove the toadstools and bin them. wear gloves though. You wont get rid of the fungus that's in the soil though as it will be a net- work of fine thread like structures [mycorrhiza]. We need the fungi to help keep the soil healthy.

It's a type of cup fungus, good and essential to a healthy soil ecosystem, but not edible so far as I know.