I would say that "Thomas" is part of a compound subject which altogether would be "As treasurer of the club, Thomas..."In other words, the subject includes some extra information about Thomas, that he is also "treasurer of the club".
Given that the word we should describe is DUES, the correct answer is C. a direct object. You can easily determine this by asking the question - What? What does Thomas collect? Dues. This way we know that it is a direct object.
