The Scabbard is used to control the Sword in some way; an equivalent function to that served by the Eagle's Claw for the Stone. This is much less relevant when handling a Sword fragment of matching alignment but clearly important when handling one that is potentially opposed. For the party, this will be important when seeking to control Rakos.
The New White Council retrieved the Scabbard from Persephone's Garden in the realm of Hades. This was done in response to clear direction from Odin that without it we would just be 'collecting pretty bits of metal'. Moreover, the actual retrieval mission was a quest placed on Dafydd to attone for his deliberate channelling of Hel's power when he read from Cillian's book of prayers in order to defend Fountainver.