Hello, these are short-tailed shrews. As for eradication, I’m unfortunately unfamiliar with control methods. If there are many of them, you may need to consult a lawn care expert or pest control specialist. Otherwise setting snap traps or other type may be effective. Home garden centers or big box stores also carry a variety of products that may help, but can’t personally recommend any one product.

You're welcome. I don't believe there are other people that study mammals on this platform through MSU Extension, unfortunately. However, these are short-tailed shrews (Blarina brevicauda). Please see these two links for a comparison. Moles have extremely large paddle-like front feet and are quite a bit larger overall. Moles also tunnel underground and create raised mounds of dirt in the lawn; short-tailed shrews will create runways through the grass as it appears in your picture.

Short-tailed shrew identification

Eastern mole identification

Another distinctive feature of shrews is that the tips of their teeth are reddish brown, caused by an iron compound deposited during growth. Moles lack this trait, so if you still have any of the specimens, this is a sure way to distinguish the species.

Doing a Google image search using their scientific names (Scalopus aquaticus for eastern mole and Blarina brevicauda for shrew) will provide a wealth of good comparative images as well.

Unfortunately we also don't have a pest control expert on this platform through MSU Extension, so you will have to search elsewhere. Apologies.

 Best,