These are fungal hyphae (strands, part of the "body" of a fungus). It suggests that some fungus is helping to break down/decompose old dead roots of a tree recently removed from the site. Did you have a tree removed from that area in the last few years?
These hyphae tend to make the soil hydrophobic and hard to wet. Grasses growing in the area may dry out and die as a result...possibly the reason you dug into the lawn?
Fungicides sprayed on the soil will not control these fungi.
Do you have any suggestions for mitigating or getting rid of the fungi?
Did you have a tree removed from that area in the last few years?
Are parts of the lawn drying out and look dead?
Yes, a large shrub was removed years ago. The grass is not drying out or dying . Thanks for your help.
The fungus is just performing its role - decomposing dead organic matter (like the roots of your removed shrub).
Since the grass is not suffering any, suggest you leave it alone.
Headway™ or Heritage™ fungicides applied by a lawn service may have some effect, but results appear mixed.
Thank you for your advice. I will let it continue the decomposition!