My deleted text messages keep getting restored. How do I delete them permanently?

I have an iPhone 5 running iOS 7.

When my camera capacity seemed to be alerting me of limited space more frequently (and with less and less photos taken), I decided to check my Settings>General>Usage and was mortified to see I had 23.3 Gb of data in Messages (dating back 2 years, even though the phone is only a year old).

I actually spent two hours (while being driven to the airport) manually deleting every text message thread. My right thumb may have arthritis now. (No. But my sarcasm says so). Yet within one hour, every single message was back on my phone. To say I was slightly frustrated would be an understatement. I wanted to punch a llama in the face. But that’d be bad form, and unnecessary. My wife has encountered the same issue on her phone too (but doesn’t want to punch a llama).

Would anyone know:

A.) A reason for these messages to reappear?

B.) A method for freeing up this space?

C.) A support group for Llama Punchers Anonymous?

I can't seem to find any answers on Google, and Apple seems reluctant to practically solve anyone's questions (or provide a simple "delete all" function).

Thank you in advance,

• Christopher (who loves llamas)