I was tossing them in my box at home. But on other plays I ended up selling whatever and it only made me keep main items. Seems safe but really id toss them in a box just incase.
Also seems vendors keep some of them. Such as the wanted board quest from D city think like most of my settler vendors are selling it as well as other main vendors.
Looks like they keep them anyways incase you wanted/needed to see them again anyways, the main ones at least. Don't certain items for cosmetics in houses get stored there too? not sure...like the eyebot model, and games...