Many people today including adults don't say thank you whether in a note (most appropriate) or even a verbal thank you. They may have said it to your child when the gift was given if your child gave it to them but I think a nice thank you note to the parent is good too. It is just one of those polite societal things that is being lost. I am on a push to have my children write proper thank you notes letting others know how much they appreciate the thought and the care that went into picking out the item for them. I refuse to let them open the toy, book or spend the gift card until a thank you note has been sent.
Maybe a polite, "I was just wondering if you received the gift my child gave. I didn't hear anything from you so I just wanted to make sure you got it." would push them a little. Yes, it is a gift for their work but a thank you is always polite.