Why won't my iPhone and iPod delete messages?

So I got a new iPhone and I transferred everything from my iPod to my iPhone but the messages on my phone and iPod won't
erase. I have deleted everything on the iPod except the messages. How can I delete the messages on both the phone and iPod?

I know an easy-to-use program can help you. You can try 4Videosoft iPhone Transfer Platinum. This program can't only help you transfer files between iPad/iPhone/iPod and computer, between iPad/iPhone/iPod devices, but also can manage and delete the SMS/contacts directly.