Translation:I came to Japan last week.
The problem I have with how duolingo handled kanji is that I don't go "aha!" when seeing them the same way as I go with hiragana. Some I know the meaning and the sound of, others I really don't know how to say in any context let alone how to say it in every context, and some I just have a clue what they sound like or what they mean. It is so hard to take them in. And most of the time when they are introduced it's "this kanji sounds like this" and I'm like "sure, ok? This weird collection of shapes sounds like that" and then I forget, because there is no context. And then they go and say "this weird collection of shapes means this" and I'm like "oh, ok, so this word is written like that, so how do I say it?" and then eventually I have a full sentence of weird shapes and I'm competently lost. It takes so long to figure out what the konji mean and then I still don't know how to say it. What duolingo needs is lessons that really connect sign, sound and meaning together. But each time there are only two out of three of these being connected.
It depends on if "last week" is topic or not. If the conversation is about what happened last week, then yes, but if it is about you ("Hello, my name is John Smith. I came to Japan last week.") then it is new information and should not be marked with は. Duolingo, of course, never gives us the context, so it is impossible to tell... :)
It is fine to add は and say
It is also fine what Duo said here without は。 It just depends if you want to mark the topic as 先週 or not, for perhaps the next few lines of dialog if that. I think even sometimes in conversations things can just get skipped too, due to "lazy mouth." It's always easy to ask a question to re-sync the uncertainties of the conversation. The Japanese do it all the time when they speak to each other.
One thing for sure, the Japanese in JP-> EN is much more "loose" and vernacular compared to say the Japanese in CH -> JP. I think that is a good thing. You will hear it in all sorts of different verbs forms and question markers in real life. It is better to just start getting used to it. Obviously, that course is meant for Japanese to learn Chinese, and the Japanese have their own language down pat like us Yanks, right?
There you will see the textbook-perfect Japanese that is needed to learn Chinese and pass the translation exercises. All of the がs, はｓ、にｓ、をｓ are placed where they should be. Try out the CH -> JP if you are interesting in seeing if from the Japanese point of view, in the language where they borrowed a lot of their vocabulary and written words. It just went alpha about a month ago ( still too soon in my opinion, but it has to go alpha at some point ) and it only has 3 not so long stages