Translation:I exit the hospital.
Its probably just not added as acceptable translation. As always, report it. As for the commentor below, you might use "a hospital" instead of "the" if you're talking to someone who might not know which hospital you left (talking on the phone).
"What are you up to?" "Going home, I just left a hospital."
If you said "the hospital", they might assume a local one, so you can intentionally keep it vague to draw more emphasis on the fact you were just at a hospital, and not the fact you're leaving a specific one. I'll admit, its not incredibly common, but thats a use case.
This is the intransitive/自動詞 version of this verb, 出る、with which を is used to mark the 'spatial mobility context' rather than the direct object of the verb (which an intransitive verb could of course, not have.)
If you sit and think about this for a minute it probably makes sense; when you exit a hospital you're not really acting on the hospital; you are exiting and the hospital is the location that action is taking place in. So 病院を出します doesn't really make sense.
I spoke to a Japanese linguistics professor and he said this is incorrect. Here was his response:
"Direct object is a syntactic category which is ALWAYS and ONLY marked by を. Semantic relations are another story though—it's true that it's not a patient, the role that tends to correspond with a direct object "place being left" is best considered a source, which would most often correspond with a "from" phrase. https://en.wikipedia.org/wiki/Thematic_relation#Major_thematic_relations "
It sounds like the professor has a more thorough understanding of it than I do, but i'm not quite sure what information you're trying to convey. I don't disagree that the direct object is always marked by を; I wanted to explain why a verb that traditionally doesn't accept direct objects appears to be accepting one in this sentence.
Is his correction that this sentence is in fact accepting a direct object? Is it that my characterization of '病院を出します' as an incorrect sentence is wrong? Or is it that the purpose of this particle is not to mark the location through which motion takes place?