Kill the food source (grubs) then they'll move on to your neighbors house.
My understanding is to get rid of moles, you need to get rid of the grubs they are feeding on.
The two answers above are correct, to limit the impact of pests and varmints you need to remove the food source, however I've found a multi-tiered approach to work best long term. If you prefer a natural, non-toxic solution, then castor oil is your answer. Looking at the product ingredients of natural mole-control products sold at the big box stores, you'll see that castor oil is the primary ingredient of the pellets and powders marketed as mole control. I went straight to the source, purchased a gallon of 100% castor oil online, and used it directly on my minor mole problem with success. The bonus for me was that it works as a rat deterrent as well. The key to any smart pest control solution, though is to combine several methods of control/management for long term success.
Milky spore is spread in early spring and again in fall. If done early enough in spring it can knock down the grub population quite well and multiplies over time. So it’s a long night term problem solver. For the short term..castor oil....in a two gallon spray container place 1/4cup castor oil, a T dawn detergent and fill it up w water. Spray when a gentle rain is expected that will spread its coverage down into the soil. I start spraying where I first noticed damage and spray outwards in a circular path...wait a week and do it again. Good luck