The correct option is C any
The correct answer is Option C.
We are to complete the sentence with the correct adverb.
Option A -VERY is used to indicate emphasis.
Option B-TOO is used indicate excessiveness and addition.
Option D-MORE is used to indicate meaning of greater amount.
In the given sentence, the speaker wishes to ask whether there is even a slight improvement in the listener's health. None of the options given above bring out this meaning and hence they are incorrect.
Option C-ANY means slight and is used to refer to one or some of a thing.
Hence this complies with the meaning of the sentence and is the correct answer.