Shirt was my first impulse as a translation, too, but if you think about it, it makes sense to say "we don't wear t-shirts here (because we wear more formal tops)" compared to "we go shirtless here!"
I know just commented on another thread about this same topic, so I apologize for bringing it up again, mods! I had another thought, though, and I am not sure how to get back to the other thread to edit my comment.
For me (AmE), "shirt" has a connotation more closely tied to "t-shirt" than to a shirt with buttons. I wonder if this is because t-shirts are much more common in North America than in Europe, so our idea of a general shirt is much more casual? And if I recall correctly, the duo picture of a "shirt" at the beginning of the lesson shows something that looks much more like a causal t-shirt without buttons to my eye.
I don't know how you would go about translating anything differently, though. Just trying to help explain why we are all so confused. :)
Thanks for the thoughtful comment. I imagine other native speakers will continue their dissent, but even the AmE-centric M-W leans towards including "a collar, sleeves, a front opening" for "shirt", albeit with the usual "usually" loophole. Perhaps the actual usage deviates. I am not going to be sorting that out for you English speakers; above my zero pay grade.
We are slowly adding the more universal "shirt" (in one of its possible meanings as a collarless and buttonless top-body garment) to the recognized translations of tri(č)ko in this course.
But I am leaning against accepting it in this exercise. As you pointed out, the Czech sentence does not promote shirtlessness but rather more formal tops, so by recognizing "shirt" we would allow a significant meaning shift. (In some contexts the meaning could be trickier, say for a place favoring toplessness, but even there I would expect the Czech original to include "nic nahoře" in lieu of "tri(č)ka".)
A deeper and welcome item for course design: This unwarranted meaning shift for narrow/wide meanings of ambiguous words like "shirt" may present a useful recipe for narrowing down their meanings in other exercises. (The contextless nature of Duolingo makes many things impossible to teach, so I welcome anything that helps remedy that.)