Q: Does it make any sense to control grubs with insecticide in an effort to make moles leave my lawn? 

A: In a word: no. Killing grubs only makes moles search more frantically for other things to eat, such as earthworms. They also eat soil-dwelling springtails and other insect larvae. In my opinion, mole traps and poisons are too complicated and exacting to use. I maintain that the best way to control moles is to persistently mash down their tunnels so they find other lawns to hunt food.