Translation:The mushroom soup has a strange taste.
Correct, but plural rules differ between the languages. I.e. sometimes Italian will use a plural in a place that English would use singular. This is such a case: you must change the number when translating; it is the only option. ("Mushrooms soup" is grammatically incorrect, as is "zuppa al fungo".)
My translation: "The mushroom soup tastes strange." seems to be another example of DL wanting literal rather than colloquial translations. Does it grate a bit when such a simple sentence is not accepted? My head immediately said to translate it that way rather than the DL accepted way. Does anyone else have a feeling that the simpler translating becomes the more DL tries to fool you? Maybe it's just me...
The original sentence with the article included is more appropriate for a situation where a place has a menu or a variety of different foods and one has tried the mushroom soup specifically. Dropping the article, then we would be talking about mushroom soup in general and it would have to be removed from the original sentence too. It is one instance where the translation doesn't work unless the article is translated as well.