The sentence is trying to convey that the attempt was being made to cover something but couldn't succeed. So, it is completed as follows: 

• Despite his best efforts to hide his anger people came to grasp that he was annoyed. Hence, option D is the correct option.
• Option A is inaccurate because the phrase within the option will make parts of the sentence contradict themselves. 
• The parts ‘despite his best efforts to hide his anger' and ‘we could detect that he was very happy’ are contradictory because the second part implies that the person has succeeded in concealing, which conflicts with the word ‘despite’. 
• Option B is inaccurate because the phrase ‘he didn't give us an impact of his agony’ is additionally contradictory because it means the person was trying to grant the impression of his emotion but failed.
• Similarly, option C is wrong because the phrase within the option implies that the person succeeded, which is contradictory to the meaning of the word ‘despite’.

Hence, option D is the correct answer.