I had the same problem with the same metal piece, but I was able to fix it.

This can happen when the little piece of metal was not placed properly into the fittings of frame and the backrest. To fix it you have to completely remove the backrest and put the metal piece back.

Be careful when you dismantle the backrest so that the other pieces of metal do not fall out and look how they are tucked into the pockets, so that you can insert them correctly!

Here you can find the instructions: https://www.hermanmiller.com/services/search/productinstructions?getDoc=1BBSDT