Thanks so much for your recommendation.

But as it turns out, it's not needed.

All one needs do is rake the things out. They will stop appearing on their own schedule after they exhaust their food -- decaying organic matter -- in the soil.

why not identify them and if good edibles, eat them? Fairy rings are often a good edible called Mirasmius oreades. Fungi can be loved!

(NEVER eat mushrooms you are not certain of identifying, and never eat mushrooms where nasty chemicals have been used. You can learn how to identify mushrooms by taking a class - in Seattle area it's the Puget Sound Mycological Society - in other areas the Extension Service can point you to a class. Knowing and hunting srooms is a great hobby and when you find them in your grass it's a gift!)