The correct answer is pester.
B. make distinctive
The correct answer is (D) To pester; to harass; to nag; to annoy persistently; to worry, tease, bait like a badger.
Badger probably comes from badge (referring to the white-marked forehead of a badger).
Examples of use:
- He could not risk being accused of badgering the witness.
- The child badgered his parents until they purchased a cell phone for him.