Companies vary a lot. We had one that would collect a week later but asked you to return them if it was later than that. Another said we'd paid for them anyway so we didn't have to return them unless we wanted to. A third said that if we wanted to take a long time they'd give us older boxes instead of new ones.
The only ones they are all fussy about are the wardrobe boxes, if you are having any of those. They like those unpacked on the day as they cost a lot to replace.