After catching Giratina, one can return through the cave to obtain a rare item, depending on how many rooms it takes to reach Giratina's room again. In just 3 rooms, the item will be a Reaper Cloth; 4 to 15 will earn a Rare Bone; 16 to 30 will earn a Stardust. Over 30 rooms, of course, will return the player to the entrance. Riding the Bicycle seems to increase the chance of next entering a pillar room. Rare items regenerate by returning to the cave each time, and they can even be received with Giratina still in the room. In Pokémon Platinum, it will have an item and the portal to the Distortion World.
Maybe Giratina is in the same room where you are getting the item...
In Pokémon Diamond and Pearl, the item that can be obtained in the last room can be found right behind Giratina, hidden out of sight. Giratina does not have to be battled to obtain the item.
So you might be seeing incorrectly and Giratina is right there...
Otherwise, there must be something wrong with your game, as you said that Giratina asn't registered yet.