How do permanently Delete Messages?

Ok so I've looked at other threads and what I found was mostly ways to "hide" messages.

I'm using iOS7 and the most I've got has been to delete messages off my phone. I talk to my girlfriend a lot this way, so there's pages and pages and pages of texts.

My phone usage says that it's STILL taking up 1.6GB! Anyway to delete this permanently?

I swiped left(?) to reveal the delete, and hit it. But it doesn't seem to affect deleting off the phone's hard drive.