Sorry to hear this. They gobble things up so quickly - it took Pete under 5 seconds to swallow the whole latex surgical glove. So, I'm not surprised that you don't know if Ramona, Norman, Jemima, or Charlie took your wrap (love your names by the way).
Since we are new to ducks, I had no idea what would happen or what to expect after the swallowing incident. Here is a summary of the things we observed and learned. Perhaps some of this is really obvious to people who have more experience, and with 4 ducks, I am sure you have more experience than us, but maybe it will give you some ideas.
After Pete swallowed the glove, we noticed she was quieter (no morning honks and less chatty than normal), her appetite and drinking were significantly less than normal, and she was pooping less - and what was coming out was mostly clear. My guess is she didn't feel very well. So, maybe you can keep your eyes out for the duck that is maybe a little more subdued than usual.
I have no idea if this actually helped or not, but after we saw the vet who explained that the gizzard might be able to break up pieces of the glove (which was a relief because my husband and I had not thought about the glove actually breaking up -- we thought she was going to have to poop out the whole intact thing and didn't see how that would even be possible, even though it was thin, pliable, and had no sharp edges), I stopped by the farm bureau and bought a small bit of grit. Pete does forage in our yard, but I thought it might help if I just gave her a little something extra. I didn't give her a whole lot - just a few pieces in my hand. It may not have made a hill of beans difference, but it made me feel better trying.
As gross as it is, take a look at the poop and see if you see small (they were really small in Pete's case) pieces of the wrap. Maybe if you just saw that, it would make you feel less worried.
Our vet said we didn't have to worry as long as Pete was still eating, drinking, and pooping -- even if less or slower than normal. I asked him if it was okay if I hand-fed her or syringe watered her if she wouldn't do it on her own, and he said that was okay as long as she was still pooping out something. He also said we would definitely know if there was a problem -- that she would probably sit very still and her eyes would kind of droop or half close, like she was going to sleep. He said (if we didn't want to try to surgically remove it - which wouldn't even be possible if we didn't know where in her system the glove was located) we just had to give it time, and that if her body could break up and pass the glove, it could be as long as a month before it passed entirely through her system. I am sure it varies with every animal and depends on what they swallowed, but in our case, within 24 hours after Pete swallowed the glove, we started to see the little shreds in her poop. Within 36 hours, she started acting like she didn't feel sick anymore. Within 48 hours, she was back to running around full speed, chasing our other animals, quacking, eating, drinking, and pooping as normal. She was pretty thirsty, but that may be due to the molasses water and the watery diarrhea she had. I still see little pieces of glove in there, and who knows how long that will go on, but I am not feeling worried anymore. Ducks have some pretty incredible stomachs!
I really hope things work out for you. Please let us know what happens!