cutting out the back is one way - another is to back the applique with a layer of muslin or other neutral fabric which will prevent the background from showing thru. You can always use a layer of batting behind the shape, which will not only cover up the background material, but also give some dimension to the applique - cut the batting a little smaller than the shape then either stitch the raw edge or turn it under, and some free motion on top will keep the batting in place.