[Edit: Ahhh...never mind, I see the recipient encased the artifacts in Lucite.]
I have no doubt that Neil Armstrong, after his return, visited many NASA contractors and thanked them personally for their work. Maybe he did hand out artifacts, or maybe he just handed out stuff that he pulled out of his pockets when he got home.
For NASA to now, fifty years after these artifacts were handed out (with warnings that any disposal other than return to NASA was a crime?), become overly concerned with their fate, seems, well, extremely petty.
But, they do seem to be overly possessive of "souvenirs" that show up on the market...I remember some random stuff showing up over the years, and various court cases. Don't think anyone actually did time, though.