Are you sure that you don’t have it somewhere hidden inside your inventory? Especially in this mod you can have a very bloated inventory, so stuff like this can easily get hidden after sorting. I’m asking since the dialog should work as long as you don’t have the item, you can see it here for yourself:
Alternatively you can just use the in-game console to give it to you. Type this into it:
game.give “records/__recycle/recycle_item.dbr”
__recycle has two _ underscores.