I have a couple of notes that keep returning to the inbox on my iPhone even after I delete them (and delete them from trash). They don’t seem to be synced to my other devices, strangely.
This has happened once before, recently, and I think I “fixed” it by deleting Drafts and reinstalling it, but that seems a bit extreme, and certainly not something I want to have to do regularly 
Has anyone else experienced this, and perhaps found a solution?
Yes, this has been happening to me every few weeks for quite a while. Only on the iPhone, never synched to either my Mac or my iPad. In my case the returning notes were in the Archive.
When this occurred for the first time I assumed a user error but the vast majority of my actions not only move the notes to the archive but tags them too. And they were never tagged after they had returned to my Inbox, although they were tagged.
My solution? Deletion. Minor inconvenience.
The only case I know of this happening is with drafts that were created on the Apple Watch, and it can be resolved by removing and re-adding Drafts to the Watch using the Watch app on you phone.
I’ve never been able to reproduce this problem, but have seen it from time to time over the years where something get corrupted in the OS-level conduit between the Watch and phone and it resurfaces a previously processed item.
If that could explain you situation, try that first.
I do use Drafts on the Apple Watch but I can’t remember if the returning notes were created on it. The last returning note is from one week ago, the second to last from June. So it’s definitely a rare thing.
Which would fit to the Watch theory because very often when I dictate on the go it is noisy and then I use Just Press Records instead because with it I get the audio file and I can transcribe it later.
I have now Drafts set to automatically add a “generated on the Apple Watch” tag and will report. Just probably not too soon.
Well, as it happens both the offending notes this time around were dictated in the Watch app, so I’ve just removed and re-added Drafts on the Watch, and hopefully that will help!
Thanks, Mr. Tortoise
Quick update: The drafts in question have NOT reappeared after the Watch app un- and re-install, so it seems to have worked 