Carollyn's suggestion and do some white feather stitch around the edge. That's because what was really bothering me was that the turned in fabric allowance was showing through. I thought the flower fragment would distract the eye from that, but the feather stitch was a better solution. Thanks Carollyn!
I had to look up a tutorial on feather stitch, practise it for a bit and then do it. My stitches are not absolutely even, but I'm happy with the result. The flower fragment will go into my tatting tin until I find the perfect use for it.