If you take the gift and click on it to start the quest, you will get the message that you have already completed the quest. So you are not getting a second pet. Nor can you send this to a friend according to Drysc who says, "You can enjoy the epic quest of clicking the delete button on it though?"
This is really just an annoyance that causes no real in-game problems. Have you noticed any other issues with Patch 2.3.2?