Speak to Vilkas and after a few menial jobs you will get this quest. This time a family has had their heirloom stolen, and will ask the Companions to get it back for them. This is a Radiant Quest, meaning that the item you are searching for is random, as is the location where it is held.
The item I got was a Glass Mace, which I don’t consider much of an heirloom, and was being held at Sleeping Tree Camp . Do your preparation work before you leave (potions, followers, etc) and head out. Fast travel to the place if you can. You’ll likely need to kill SOMETHING to find the item, which for me was a giant, and then I picked up the glass mace out of a nearby treasure chest.
Once you’ve killed whatever is between you and the item, and claim the item, return to Vilkas and give it to him. The quest will now be over and you will be 300 gold richer.