Yes,a bunch of sprites like that is horribly inefficient and should be avoided. There is no reason to avoid tiled backgrounds. Just move your source image up one pixel and it will solve it.that extra line is wrapped around from the bottom of the image. So don't move the tiled background up a pixel. Open up your source image and nudge it up one pixel.
Otherwise, just reduce the height off that tiled background by one pixel to cut if the wrap-around.