I also slid the hanger into the bracket and heard it click, without mounting it and before reading this thread. I tried to loosen the tabs by inserting a screwdriver through the two open slits, but no luck. Maybe a longer and slimmer and more rigid screwdriver is needed? I managed to get the thing apart without breaking it by gently pulling apart at the top (i.e., the part above the Tesla symbol). I don't know if that's the best way, and I'm not recommending it, but it worked for me.
When it was clicked in place, I wished I had a photo of the two parts, so I'm posting one here for anyone who gets into this situation.
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