As a quest item, it has no weight and so there is no consequence for having it in your inventory. I do not know exactly how one would "get rid" of it, but I will do the two best things that I can think of...
First, I will look into it. I may be able to find out a way. I am not quite "there" in skyrim. Mostly due to Morrowind always pulling me back in and a wierd obsession with cheese... But, I'll try to rush it, so that I do some play testing.
Second, I will perform the powerful "Dance of Summoning AzuraKnight"! Who's knowlage of all lore in Skyrim is unchallanged and surpassed only by his might and mercy... In the hopes that he may teach us the truth of these things...
- Nomar the Nomarian begins the complex and whirling steps pf the ancient dance used to summon AzuraKnight!