Bank services of MoneyGram on money transfer are available only to individuals. MoneyGram MoneyGram hired compliance officers in many of their global offices to ensure compliance with regulations of specific countries or regions. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. The benefits of money transfers by MoneyGram: the opportunity to send a telegram with money transfer (up to 10 words) for free. MoneyGram completed the rollout of simplified pricing for money transfer services in the U.S., an initiative that began last year.