"She does not like the color blue."
Translation:Nemá ráda modrou.
I am not sure if it is possible to ommit the "color" in English. However it is in Czech and both "Nemá ráda modrou" a "Nemá ráda modrou barvu" are just fine but it is more common to use it without the word "barvu".
Secondly, article "the" definitely can't be translated here. There is only one "color blue" and therefore there is no need to point at it and say "tu modrou barvu".
It is uncommon to hear native English speakers say "the color blue," as blue can be nothing but the color so it's well more than possible to omit. It can be said, but it is a more formal tone. Otherwise, it's redundant and awkward.
I am a native English speaker and I agree. You can say either "She doesn't like blue" or "She doesn't like the colour blue". The first is more common and natural, the second is more formal but still used. The phrasing in Czech given here would seem to suggest "She doesn't like blue".
Z jakého důvodu je chybně: "Ta modrá barva se jí nelíbí."? S oním "the" to vypadá, že nemá ráda jen určitý odstín modré.