It looks like the whole seam allowance is frayed away so you can't just hand stitch it closed without pulling. I would hand stitch a white piece of fabric that matches as close as possible, about 1 inch from the frayed edge. The end pieces will have to have the seam opened up a bit on each end of the strip so you can insert the ends of the strip under them. The seams can then be hand stitched closed again.
I would add more quilting so the layers have less movement when it is washed again.