I was thinking more about objective covers as none are supplied.
D
It would be pretty hard to design a one-piece objective cover to stay on your folding pocket bins when both unfolded and folded, and a two piece design with tethers so you don't lose them starts to over-complicate the concept of a convenient pair of bins in your pocket. And therein lies the probable solution to your bins-protection issue: fold them up and put them in your pocket.
Lee