The benefits of money transfers by MoneyGram: payment of commission is only at the expense of sender. FormFreeSM phone-based offering allows businesses to reduce labor costs and create an excellent consumer experience by leveraging MoneyGram Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. The Global Funds Transfer segment is the primary segment of MoneyGram, providing money transfer and bill payment services to consumers, who are often unbanked or underbanked.