I think the question was - what to do at the end of the row of stitching?
I don't backstitch very often - I usually sew two or three 'stitches' between units if I'm chain piecing.
Sometimes I tie the threads in something that won't have another seam crossing it.
I would stay-stitch the outside edge of the piano key border to keep the strips from pulling apart.. Stay stitching is just a line of machine stitching about 1/8 inch from the edge.