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Even if it works to delete the conversation to reclaim space, it's not really a solution. I don't want to delete my conversations? I just want to delete all the attachments, images and videos in my conversations to reclaim more space.

Messages -app or Settings should have a "Clear messages attachments" that'll delete all attachments. Also perhaps a "Export messages attachments" that we can use before clearing the attachments to save all the attachments to somewhere - dropbox perhaps or send to Mac.
 
If you use the iBackupBot method and want to save the messages, just delete the attachments (this includes those "hidden" that make up the dead weight, for those of you who have that problem) instead of everything in the folders mentioned.

- Make a backup in iTunes
- open iBackupBot
- go to the relevant backup
- hit Other Multimedia Files (you might have to click on the tab afterwards, in case it goes straight to camera roll instead)
- sort by filename by clicking the Filename tab
- go to MediaDomain/Library/SMS/Attachments and highlight all of them.

Now you can delete them all by right-clicking and choosing delete (you might want to export them first, up to you), close iBackupBot and restore to backup in iTunes.

Tadaa! Space recovered, texts/SMS/messages (whatever you call them) still there!

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Thank you for this. Sounds like a pain. I'm hoping that now this issue comes to light enough people will complain that Apple will figure out a way to fix this with a software update.

If not I'll eventually try the ibackup method.

Well, it was fixed a long time ago. This problem affects only those who deleted threads containing attachments while use the version(s) of iOS where the attachments were still there. So in that sense, it's way too late to tell them to fix what they've already fixed ;) But I do agree with what someone else (or you?) said about the need for a "delete/export attachments" option!
 
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