Don't use sugarless gum... most contain Xylitol...very toxic to dogs. There is a natural treatment for grubs:
Organic Lawn Pest Control: Milky Spores and Nematodes | DoItYourself.com
Milky Spore and Nematodes. May take up to 2 seasons to work, but lasts for years. My lawn is on year 4 or 5, and I used to find grubs everywhere. Haven't seen one for a year or two. And no moles or voles.
Just sprinle it on the lawn and water in or wait for rain.