I would not recommend key rings. While you may find them easy to get off, I don't think the TSA gives those screeners much time per suitcase and I believe in easy access for them. (I have NO proof of this, I just kind of try to think about what will make the TSA person happy. I figure if they don't like my suitcase they might spend so long searching it that it misses the plane!)
There are some suitcases which if not locked may pop open all by themselves if you drop them just a little. They are the kind where you stick you rfinger under the latch and pull outwards and the latch makes a little snapping sound and pops out diagonally. Then, if the suitcase is on the floor, you stub your toe on the latch. Ouch!
I don't know what you use to hold these closed other than a strap.
About the strap they took off and didn't know how to put back on and now it is missing, have the airline buy you another one. Use both the airline's claim form and the TSA's claim form anyway.
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