Question, where do you live? In America, and especially on the Pacific Coast 'Have a great day' is a phatic expression [1]. It is a common parting phrase and has lost any special significance that it might have once had within a conversation.
I live in the UK where parting phatic expressions such as 'cheers', 'see you later', and 'take care' are common. But 'Have a good/great day' definitely is not.
and ngl yes of course I read it as something else first.
Anyway maybe they were glad that someone threw them even a phatic expression at all? :)