MSU Extension has published several helpful articles on mole deterrence and removal. I've linked these below and hope you find them helpful. Sometimes the most effective tool in one situation is not effective in others so you may have to try a few of the proposed methods outlined below. Sometimes physically trapping the moles is best, sometimes it's grub treatment, sometimes it's poison. Also, these articles discuss options for both eastern moles and star-nosed moles.

What to do about moles

Moles in the lawn

Reduce lawn and garden damage

Best of luck.