"This skirt has no pockets."
Does it? From where I'm sitting it says ありません -- but anyway, the difference between 〜ないです and 〜ありません is interesting. Just for context, ない is the (irregular) negative form of ある (to be), and like all negative forms of verbs, it acts just like an い-adjective. So there are two pathways we can take to making ある (or any verb really) both polite and negated:
ある -> ない -> ないです -- make it negative first, and then polite.
ある -> あります -> ありません -- make it polite first, and then negative.
It turns out, the last thing we do has the most emphasis. So ないです puts a little more emphasis on the fact that we're being polite, while ありません puts a bit more emphasis on the assertion of negation.
I remembered there was a good post on this somewhere and I managed to dig it up again: https://japanese.stackexchange.com/a/2577
ありません, being the negative form of あります which is the polite form of ある is already polite, you don't need to make it more polite by adding です. If you want to be slightly more polite and put slightly less emphasis on the negation, use ないです.
Or did you only see ない? If so, that's strange, because it's not what I see... maybe different people are seeing different versions of the question.
My guess would be that people who see this sentence in the course would have ないです nowadays it's the most polite/common form. But people who already completed the course and see this sentence for the first time in the strengthening exercises like I just did may be offered only ない so that we can learn a new level of politeness while practicing?
You use は to mark the topic of discussion. It can be used in both positive and negative sentences. You might imagine 「Xは～」 as being translated like "As for X..."
お金はない。"As for money, there is none."
By contrast, が sort of answers the question "which?" so you might translate 「Xが～」 as "X is the one that..."
お金がない。"Money is what we don't have."
Here the emphasis is on the fact that it's money specifically, to the exclusion of other things, that is what's missing.