I have this same problem. I contacted Apple Support. They told me to either,
A) delete messages one at a time
or
B) restore to factory settings
I've copied and pasted our conversation below if you'd like to read their suggestions.
-------------
Thursday, February 20, 2014 12:24 PM
Duration: 38 minutes 19 seconds
Douglas:
Thanks for contacting AppleCare chat support. My name is Douglas. How can I help you?
Douglas:
Hi Greg! How are you today?
GREG:
Hello, I need help with my iphone 5 ios7
GREG:
i've been searching the support communities and ahve not founda resolution
GREG:
I am trying to remove the "Messages (SAVED)"
GREG:
under general settings
GREG:
many threads in forums, lots of frustrated peeps, no solutions
GREG:
can you help me remove 4.0 GB of messages?
Douglas:
I'm sorry to hear that you are having issues with your iPhone and saved messages today today. I know how important it is to have a working iPhone and all of it's features. I will do my best to assist you today!
Douglas:
But before we get started, your case number today is, xxx536, if you need to reference this case in the future or need any other assistance, we offer a lot of resources via our support website at http://support.apple.com.
GREG:
I've been there, thanks. couldn't find help. that's why I'm typing at you now. 🙂
Douglas:
Understood, I will do my best to assist you today!
Douglas:
Greg, in order to help guide us in troubleshooting today I’m need to ask a series of questions. If at anytime you are not satisfied with any troubleshooting steps or a resolution, please do not end the chat. Let me know right away so I can look into other options for you. How does that sound?
GREG:
🙂
GREG:
hit me
Douglas:
Can you help me understand exactly what “Saved” messages you are referring to? Are they preset messages or messages that have actually happened but do not seem to be leaving the phone when deleted.
GREG:
present messages
GREG:
under Settings/General/Usage/Messages 4.0GB
Douglas:
Ok, thank you for that information! Bear with me a few moments while I look into this for you.
GREG:OK
Douglas:
Thank you very much for your patience Greg while I looked into this for you.
Douglas:
Do you have a lot of saved text/sms messages on your phone?
GREG:
I do. I do not want to go thru and delete them one at a time, that would take forever.
GREG:
is there a way to simply delete ALL attachments in my text messages?
Douglas:
Let me check on that for you. Be just a few moments.
Douglas:
Just a few more moments. I will be right with you.
GREG:
k
Douglas:
Thank you for your patience. I will be with you shortly.
Douglas:
Thank you very much for your patience Greg.
Douglas:
From what I can see on my research it does appear as though you will need to go through each text individually to remove them from your phone.
Douglas:
The only other way to do it would be to restore your phone to factory and set it up as new.
GREG:
really? either take hours deleting each text message individually, or restore as factory and lose all my data?
GREG:
that seems like two impossible options
GREG:
Aren't everybody elses' iphones filling up too?
Douglas:
The best way to do it actually would probably be to backup your phone to iTunes and restore to factory. This way you will actually still have all the text messages but your phone will be clean and allow you to have full capacity again.
GREG:
what data would I lose if I restore to factory?
GREG:
also, I just did an icloud backup this morning
GREG:
so what are the steps I would take to do this?
Douglas:
You would remove all of your pictures, texts, videos, etc.
Douglas:
For the most part your phone would be as it came out of the box when you bought it.
Douglas:
Since you use iCloud we would turn that on so that all of your contacts came back to it.
Douglas:
iOS: How to back up your data and set up your device as a new device
Douglas:
iTunes: About iOS backups
Douglas:
iOS: How to back up and restore your content
Douglas:
These are some great articles to help guide us through the process.
Douglas:
And to answer your question about other people I’m sure they too are seeing some storage loss due to text messages however, I know a lot of people that delete their text messages regularly.
Douglas:
I however, and not one of them. I am up to 3.2GB
GREG:
Wow, seems like drastic steps to take to resolve an 'oversight' on apple's part. Can you email me a copy of this conversation so that I can read it, have links saved, etc. ?
GREG:
FYI, many folks on the forums are deleting their texts and STILL have GB's of space taken up as Messages (SAVED).
Douglas:
I sure can send you a chat transcript. I will also be emailing you these articles so you can have them that was as well.
Douglas:
That is very well possible. The forums are a great source of knowledge but what happens in most cases they don’t contact us to let us know there is a problem or concern. I do appreciate you taking the time out of your day to inform us of you issue.
GREG:
Do me a favor, if you come across an apple update that confronts this issue, let me know.
GREG:
Believe me, YOURSELF will have this issue soon too, I assure you.
Douglas:
I believe you. You know what you could do to help us?
Douglas:
You can submit product feedback about this at [apple.com/feedback apple.com/feedback] . We have a team here at Apple, who's entire job is dedicated to reviewing this feedback, and escalating it to the proper outlets (such as the engineers for iTunes, iPhone, iPad, etc.), so you can rest assured that your voice will be heard! The more feedback we receive about product features, the more likely we are to implement them! I'd be more than happy to walk you through submitting feedback today if needed!
Douglas:
That link should just be apple.com/feedback Not sure why it entered twice in the chat.
GREG:
is it considered iPhone feedback, or iOS7 feedback?
Douglas:
I would consider it that yes.
GREG:
OK, I'll click around and submit. Thanks again. Please email a copy of this.
Douglas:
No problem, the transcript will mail to you once the chat ends. I will also be sending you a case number as well for you records.
Douglas:
Is there anything else I can help with today?
GREG:
nope. thx
Douglas:
Great!
Douglas:
It's really important to me that you're happy with your experience today. Before I let you go, I want to make absolutely certain that you're satisfied with me and the support I've provided today. If you're not for any reason, or have any outstanding questions, please let me know.
GREG:
you were fine, thanks. this is a design FLAW that could be easily addressed in an iOS update. I've already started filling out the feedback form you suggested. thx again
Douglas:
Awesome!
Douglas:
Greg, I would like to thank you for contacting AppleCare Support! I will be emailing you your case number and if you have any additional questions, don't hesitate to chat us again and the next advisor will be happy to pick up right where we left off!
Douglas:
Again my name is Douglas, if you are satisfied with the service I have provided, please use the “End Chat” button in the bottom of this window if “end chat” is not available let me know and I'll be happy to end the chat for you. Hopefully you enjoyed my service. Thank you for contacting Apple, have a great day!