Correct, I've scoured my mobile facebook and nothing is getting rid of it.
I had the same problem and hated it.
What you have to do when you open a message is let it load 100%. If you don't open it all the way, it's like the app thinks it hasn't been opened.
You will need to go back a ways and open a few because you probably don't know which messages are 'not yet opened'.
Obviously to prevent this in the future, let all messages load all the way before exting..