Most say may. Indeed I think the only one that doesn't you would maybe find annoying is the one that restores an item and its only 1 card in 12, and its easy enough to manipulate the turn deck to add extra cards if needed
The one I find annoying is the one that gives you two options and one is to discard a Quirk card. All my Quirk spaces were filled with cards that didn't really affect me. Then, of course, I draw the Tormentor who can be quite a pain especially as I 'm playing solo with the Specialist who isn't the best fighter despite tweaking his deck here and there.
You have to take it unless the loot says *may*