Originally Posted by
Genden
After seeing the picture, I would hand embroidery in satin stitch with thread that exactly matches the fabric to close the hole. No one will know it is there but you.
I'd take several of these suggestions and blend them:
Bo-Nash makes a fusible powder, I'd work some powder into the hole, cover the hole with parchment, hit it with an iron to fuse it. Then I'd dab some Fray Block around the edges, you wouldn't want them to fray after several washings. Then, as Genden said, I'd embroider over the hole with thread the same color as the background fabric.