If the grubs are eliminated the moles will just feed on the earthworms. I use those mechanical traps which work about half of the time. It's a never ending battle.

Moles do not limit their diet to just grubs. They are insectivores and eagerly consume any soil dwelling invertebrates they find - grubs, centipedes, sow bugs, larvae, earth worms, slugs and snails. In fact, a lively mole population indicates a healthy, biologically rich soil, exactly what you want for a vigorously growing garden. Killing off their food source will also have a negative impact on your garden as well.

The fact that they can trash your lawn is a given. Unfortunately, the only successful way of depleting their numbers is by trapping. Or owning a cat that is a serious hunter. Nothing else works, especially dozens of so-called "natural" remedies, so don't waste your money :-))

I have no solution, but following to see it others do.

I rarely have a 50% success rate with the 3 types of traps I use and aggravating.

Everyone pooh poohs me about this, but I've been using sound emitters for 25 years! Up until 8 years ago, I lived in gopher city! I did use hardware cloth for gophers, but they would still show up in the paths! Started with battery operated buzzers. Then went to solar ones that now don't even buzz! They just vibrate! It does take the little buggers a couple of weeks to figure out that the nasty noise isn't going away! But then they're gone!

We've been at our place for 8 years and the neighbors have gophers, but we don't! Even with raised beds without hardware cloth!

Gophers aren't moles.

But they both respond to the sound emitters! They are actually called mole something or other emitters, not gopher emitters, but work for both! Work for voles, also!