Your yard may be the perfect habitat for an opossum. If so, you shouldn’t expect it to leave and go to a site with poorer habitat. In this case, you have the following options.
Before anything though, I would make sure you have an opossum and not a raccoon, skunk, or bird damage. Possums are not known for extensive grass damage like a raccoon or skunk. Details on identification can be found at Damage Identification
1. Wait till the food source has been consumed and make sure you prevent the problem next season.
2. Degrade the quality of the opossum habitat in your yard. Spraying pesticides for grubs may help but frankly, they often work too slowly to stop the damage immediately. So you may have to wait till next year anyway.
3. Electric fencing is effective but may not be legal in your town.
4. Trapping. Consult your local laws to see if it is legal and what requirements there might be. Techniques on trapping etc. can be found at the links below.
What Doesn’t Work.
1. Don’t waste your time on repellents. They won’t work on opossums.
Prevention strategies:
1. Make sure there is no food available (trash, unpicked fruit or fruit on the ground, pet food, unprocessed compost, and bird seed on the ground).
2. Make sure the opossum loses the habitat that protects it from the elements and predators (access to buildings or sheds, access to a hide-a-way in firewood or brush piles, untrimmed vegetation, under porches). In other words, make the best habitat for this opossum somewhere else, and not in your yard.
If the opossum is injured, contact local animal control, a wildlife rehabilitator, or a professional wildlife controller.
And don’t forget to check with your local Cooperative Extension office about identifying and treating your grubs.
Resources: (online)
Opossum
Wildlife Control Advice over the Phone