Looks like each petal of each flower is hand stitched to the thin background. If you clip those stitches, you will end up with a pile of loose flower pieces. I personally think that the hand stitches are part of the charm of the vintage quilt, so I would carefully cut around each flower, maybe leaving a 1/2" border, then think about reattaching them to a stronger material, perhaps by applique. I really like the look of those flowers!