Looking at the pics again it almost looks like the maker joined. The two pieces of the leaves by just satin stitching the edges and now thru use the edges have wiggled out of the satin stitch.
You say the quilt is old, did you make it or somehow acquire it. Depending on its history you could hand satin stitch those leaves back together just working with that back fab, or as others have suggested cover with ribbon or fab stri.