Robert's necklace is an item found in the Ritual of the Mahjarrat quest. In a letterRobert the Strong addresses to the player, Robert explains that the necklace was crafted for him by his sweetheart, Ilsinor, and that it will be used to convince Robert, in his human form, that he wrote the letter. Currently, this item has no use, though it can be equipped. It appears to resemble a Berserker necklace.
If you speak to Bob about the necklace, he has no interest in it. Neite, Bob's cat girlfriend, however, becomes jealous, believing Bob has another girlfriend, Ilsinor. The matter is cleared up when you explain that Ilsinor was the human Robert the Strong's girlfriend, not Bob the Cat's.
Presumably, the necklace will have a use at some future time, when the player meets Robert the Strong again. Until then, for players wishing to save Bank space, the necklace can be destroyed, as it can be reobtained in Kethsi.