Here's a little good news. The piece of fabric- a 12 x 12" flour-sack napkin-was ruined, for the project I was doing. There was no way I could rip out the faulty embroidery.
But I found a way to salvage the fabric. When I do free-motion embroidery, I use one of these napkins for the front and another for the back. The back piece gets a ribbon casing for a hanging rod. Since the back is never seen anyway, I used the bad piece for that purpose. I am starting a new one soon-probably Valentine's Day. Yes, I know it's kind of early (or arguably, late) for that, but I've done just about every other holiday I can think of.