Hmm.. I have some of that clay
I also have about 20% of new unused Meguiars C2000 Clay which I reserve for the cars here at home.
And then there's the 7x7 Nano Towel.
I don't do anything special. I just grab a chunk of clay as I need it.. The C2000 goes back into the jar.
That clay you have there I keep in the black Meguiars clay cases that came with the clay kit.
My inner cheapo lives strong when it comes to clay, so I also save used pieces and just stick them on top of the containers [unprotected] just in case I find something like windows or wheels to use it on.
The Nano Towel gets placed in an open zip lock bag.