Q.There Is Some Creature That Has Dug Up The Edge Of My Lawn
There is no mole trails or holes.

Certified GKH Gardening Expert
Unfortunately, it can be hard to say what is causing the damage without catching the culprit in the act. What I can recommend is using hot peppers, or capsaicin to repel pests. Mammals will usually leave the area when they smell the pepper oil.
This article is for making the oil for fruit trees, but the process will be the same, regardless:
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/hot-peppers-for-fruit-trees.htm