Does cardio exercise burn the fat off the inside of the arteries?

No. The deposits on the inside of arteries are actually mostly made up of white blood cells, particularly macrophages. It is not made up of fat cells whose purpose is to store and release energy. There is a connection between diet and atheromatous plaque, to be sure, but it's not so direct as the fat you eat getting stuck on the inside of your arteries. It has more to do with how LDL ("bad") cholesterol affects macrophages.