No. It is not what you thought.

賀 never signed a paper 把賀梅送人. Instead, he and his wife signed a paper to let Baker family to take care 賀梅 temporily. They thought they could take back 賀梅 anytime. Before 賀梅母親 signed that paper, she specificially asked about this question and got the Yes answer. The translater for her later confirmed that in the court apperance and this is one of big reasons that 賀 won that case.

In my opinion, the lower and appeal courts in TN screwed up this case bad and they did not follow the law. Baker family took advantage 賀's situation and tried to use court to get 賀梅.
This is why highest court in TN was so mad about this case and they unanimously overturned the lower court's decidion and kindly blamed the lower courts on this. 賀梅 was returned to 賀 family.