The correct option is C though
The given sentence expresses a contrast, which means that the ideas are opposite in meaning. The contrasting ideas are 'grandmother enjoys good health' and 'she is very old'. They are opposite because usually people who reach their old age, do not enjoy a very good health. For most of us, with age, health deteriorates.
Options A and C:
'Though' and 'although' both express contrast in a sentence.
They have the same meaning 'in spite of the fact that' but their usages are slightly different.
We generally begin the sentence with 'although', we do not use it in the middle of the sentence.
'Though' is generally used in the middle, after the main clause 'My grandmother enjoys good health'.
Hence, option C is correct and A is incorrect.
Options B and D: 'Since' and 'as' refer to reason. They do not complete the sentence in meaning, because the ideas do not indicate a relation of reason/cause and its effect; the ideas express contrast between each other.
Hence B and D are wrong.