How did grease get in under cooktop on stove?
Most of the dishes we cook do have at least some oils and fats in them. Even when we are not explicitly frying, or even sauteeing, the delicious fragrant vapors which fill our kitchens when we cook waft around and get into every nook and cranny of our walls, cupboards and stoves, even places where we can't reach to clean. These vapors contain tiny droplets of oil from our cooking. Over time, this deposits lots of grease in inaccessible places.

After a few years, even the blinds above the sink on the other side of my kitchen are lightly coated with a gross mixture of dust and grease. I do fry and sautee a lot, so it may take longer in your kitchen, but that's where that greasy residue comes from - through the air.