Also, quest items that are equipable (jewellery, weapons, armour) don't appear in the 'quest items' tab, they appear in their normal tab, but you still can't detroy them or send them to the battle tower.
But don't worry, they don't take up any inventory space - you can prove this for yourself, just send everything to tbe battle tower that you can (including all the stuff you've got equiped) and you will be showing '0' for your inventory usage.
