Talk to Melody, a child slave at The Fort. With a Speech check of 50, you can learn that her teddy bear, Sergeant Teddy, was taken from her by that meanie Antony. Find the mongrel breeder and talk to him about giving Sergeant Teddy back to the little girl. He will agree, but only if you fight a few of his dogs in the Legion arena. This can be avoided if you have good reputation with the Legion or the Animal Friend perk. You may also pickpocket the bear from Antony or kill him.
Once you have Sergeant Teddy, return to Melody. There are two options available: one can give her the bear for good Karma, or one can tear the teddy bear in half in front of her, resulting in bad Karma, but Legion fame.
Behind the scenes
It is possible that the two ways you can finish this quest is a reference to a quest in Fallout 2 for Curtis, where you have to recover his Mr. Nixon doll. You can give it to him or rip it up in front of him.
Prior to patch 220.127.116.114, the Legion mongrels could have 1600 hit points and be very time consuming to defeat.
Xbox 360 If Antony dies before starting the quest, Melody might no longer be present at the Fort.