That granny is actually the matchmaker, methinks. She's trying to bring your tama a soulmate, and you keep turning them down, you fickle female! <_<
(..and now I see that shadowprincess already answered that bit, so nevermind me!
)
As for the deleting an item, shadowprincess is incorrect and tamafana is correct!
1. Go to the open book icon in the lower right section of your tama screen. Scroll down and select "Present", then select "Item".
2. Scroll through your items and select the thing you want to delete.
3. Your screen will say "Wrap?". Press the A button, and it will now say "Trash?". Hit the B button.
4. The tama screen will ask you if you're sure, select A, and Voila'! Item deleted!