In the sentence, care is an uncountable noun.
Little is a quantifier used with uncountable nouns. That rules out Option D 'Some'.
Without the article, 'little'emphasizes a small amount of something.
Adding the article removes the emphasis—a little means some.
It has a positive meaning.
The little means not much, but all of those.
In the above sentence, using the article 'A' brings out the correct meaning.
Therefore, 'A little' is the correct answer.