sorry to say there isnt much you can do as if you dig it up the fungi spores will go everywear .

You asked a similar question before, Nealeie, and I asked you for certain information, which you've not given...

Afraid you will have to live with it. You can reseed the dead bit. Often you get a ring or greener more lush grass too.

Increasing the diversity of the soil organisms in you lawn often helps, Nealie. You do that by applying compost regularly, in addition to whatever other fertilizer regimen you have, and mowing a little high, and frequently. The ring will still be there, but it will be less noticable, and greener in the middle.