Final answer:
In the Harry Potter series, during a Dueling Club meeting, Millicent left a badge on Hermione's robes as they wrestled.
Step-by-step explanation:
The item that Millicent left on Hermione's robes as they wrestled at the dueling club was D) A badge. This event is a detail from the Harry Potter series, specifically, it refers to an incident in 'Harry Potter and the Chamber of Secrets' where Millicent Bulstrode, a member of Slytherin house, and Hermione Granger, a Gryffindor, are paired up during a Dueling Club meeting. During their duel, physical contact occurs, and although the books do not specifically mention a badge, this seems to be the plausible item given the context of school and dueling clubs where members might wear badges to represent their houses or clubs.