Trouble is I am not sure what I would say back to the equivalent phrase in English. In the US, if someone says "Have a nice day", I think how nice and polite people are in America. In the UK, if someone says "have a nice day", I think "how vulgar, why are they using US speak? What about a good old traditional English, now bugger off".
Rather than ask anyone I have done some web searching. I did find a research article on linguistic politeness in German-speaking Switzerland
There is even a theory of linguistic politeness, Wow I might indulge in a little "negative politeness".
die Fremden wissen nicht einmal wie man richtig grüsst' [foreigners do not even know how to greet properly.