Mrs. Peacock was blackmailed because she was accused of accepting bribes to influence her husband's vote as a United States Senator. Despite her claims of innocence, she chose to pay the blackmail money.
The primary reason for her compliance with the blackmail demands was to prevent the story from being revealed publicly. She feared that the accusation, even if false, would be exploited for a political witch hunt, potentially damaging her husband's career and their reputation. Therefore, the blackmail served as a means to suppress the potentially scandalous information and avoid a significant public and political fallout.