"I've taken off my belt."
These sentences shown by Duolingo at the top of this discussion are the exact translation pair that Dr. Okrand gave for this sentence, so they are used for the "best translation" that gets shown to users. However, Duolingo should also be marking it correct with -wIj as well. What makes you think that it would not be valid? If you thought you typed that and got marked wrong, you either made some other error that you didn't notice or there was a software bug. I don't see any "my answer should have been accepted" reports. Did you get a screen shot?
jdmcowan is referring to this article by Okrand: http://klingonska.org/canon/1993-12-holqed-02-4.txt
Okrand's translation is clearly in error or very loose: it's only inferred that the belt is my belt because I'm the one taking it off. The sentence does not literally talk about "my" belt.
Notice in the article that what Okrand describes is actually a slang expression meaning something like It's like I didn't hear you; I won't tell.
I wouldn't be so sure it was in error. Not all languages put the possessive on an article of clothing or body part that is being used personally, the equivalent of "I'm brushing the teeth" being sufficient, because if you were brushing someone else's teeth, that would be weird enough to specify. I remember being relieved when this sentence came out, that Klingon was not slavishly copying English in this respect.