Yea the whole property thing didn't really make me go 'wow!'. Cloning is against the law so to go public and try to claim a person(which is ridiculous) would be claiming something illegal so that wouldn't work either.
You're not thinking deviously enough.
You're assuming the whole clone has to be claimed as property. That's actually the last thing Dyad would want to do since what's against the law is cloning a whole human being. There is no law against cloning organic tissue or individual body parts for organ replacement, however, which means all that's required is enough tissue to get a good DNA sample, because the tag will be imprinted on DNA throughout the body. All you have to do is kill the clone and harvest the organs. If you need to present the DNA tag in court, all you have to do is present an organ as the source material. A clone is a human being. A heart is just a heart until it's inside somebody.