According to a strict interpretation of grammar rules I think it ought to be 'fewer' calories, since calories are countable, but all grammar rules really are are an identification of precedence, and the precedence in this case is for 'less'. Still, I would say 'fewer', because that's what I'm like.
To Karen, because it's impossible to target weight loss from a specific area, you have to lose weight overall. To do that you want to create a caloric deficit, i.e., to burn more calories than you consume, which means to eat less and/or to exercise more.