They seem to me to be an advertising item. The words on the box, Eats and Grease Job probably have nothing to do with what was inside. that is why I suggested something like mints, candy, gum or matches. Something that might have been given out at a restaurant or gas station as a freebie. Could be that they were distributed by somebody else and that the businesses depicted were just people who paid to have their name on the box.

As for a striker, I am probably too young to know but, is it possible that there were matches going back that far, like the blue tips that I know of, that didn't require a striker to light. You could light them on your shoe or any rough object. Therefore a striker might not have been necessary.

Both of them do have 1 thing in common. They both could be from a diner or from a couple of diners.