The correct option is
D had posted
The given sentence contains two actions, 'to tell me' and 'to post the letter'. In a sentence with a sequence of past events, when one event is in the simple past tense, the other is usually in the past perfect tense. The event already mentioned is 'told me' which indicates the simple present tense. Hence the other will be in past perfect tense.
Option C: 'Had posted' indicates an action that began and completed at a certain point of time in the past, i.e., past perfect tense. Hence this is the correct option.
Option A: 'Has posted' expresses a present perfect action, that has just been completed recently. However, the action took place in the past which is why the brother narrated it "told me".
Option B: 'Will post' refers to the future whereas the action is in the past.
Option D: 'Is posting' refers to a present action that is continuous. But, the sentence narrates a past event.
Hence options A, B and D are wrong.