Final answer:
The correct antonym for 'CRUDE' in the context of the given sentence is 'tactful,' which signifies a polite and considerate approach in contrast to crude behavior which lacks refinement and subtlety.
Step-by-step explanation:
The question asks for an antonym of the word CRUDE as used in the phrase 'made a CRUDE apology for his behavior.' Based on the given options, the correct antonym would be tactful, which refers to a behavior that is considerate and sensitive in dealing with others or difficult situations, as opposed to crude which implies a lack of refinement or subtlety in behavior or speech.
The references provided discuss an author's disapproving tone towards a subject's poorly managed behavior. In the context of these examples, crude behavior may refer to actions that are untamed and impolite, further illustrating that the antonym would be something akin to being tactful, where action is taken with consciousness to politeness and sensitivity.