Hi! I'm here in Oklahoma & my neighborhood is having a problem. We all have bermuda grass----which is a thorn in my side & takes over all my flower beds----yet I need to save it---sigh. We have had these brown circles appear. I was told by a lawn service company that it is a fungus but was given no advice for healing my lawn other than adding top soil to it. My DH did this today but we just wanted to make sure there wasn't something more we could do. The whole polka dot look is not exactly what we were going for:)
There are many products that fight fungas in lawns on the market. And it does seem strange to me they did not offer some type of chemical solution. If I was you however I would just follow the lawn service advice. Those people are expert and responsible for what they tell you to do. If it does not work they are risking their reputation.
We have had so much moisture this year I think everyone is fighting fungus and mold issues. I use Soap Shield from Gardens Alive. Spay every week at the recommended rate for turf.
However, if the fungus kills bermuda grass I may be tempted to refrain from spraying close to my garden. Just joking. Bermuda is a pain for gardens. I wish I could get another kind of grass to grow that would drown out the bermuda. I tried to plant some other grass once and it took off fine then by end of summer it had been squeezed out by bermuda. Price of living in OK, I guess.
OR it could just be that the fairies were dancing in a circle. They do that. Treatment is the same as for a fungus.