"Gutten Tag" can be transled into English by using 'hello', 'good day', or 'good afternoon', indeed. But I chose to use 'hello' because it is the most common form of greeting when meeting someone.
If I used 'good day', it would sound very much like 'good bye', which is already in the text. It is true that 'good day' is used to render the exact meaning we find in German, but that happens in very formal contexts.
And I am reluctant to using 'good afternoon' because it refers to a certain time of the day only.
It is difficult to decide without a context...