M.F.
I wouldn't be offended, but a person who feels that the grace period is just an extension of the due date probably would. A person who thinks that just because they pay in the grace period or within a week of that they are doing nothing wrong, would probably think since they eventually pay, the landlord should be happy with that and not nit-pick about when rent is received. They would probably think that since the landlord hasn't charged a late fee yet, the landlord doesn't mind and they're doing nothing wrong by paying late every month.
They would also be self-centered, irresponsible, entitled jerks who, if I was the landlord, would be reminded this month, charged a late fee every month they pay past the due date and evicted the next time they pay past the grace period.