If MoneyGram money transfer, for some reason has not been received by the addressee, the sender will receive a refund. If you need to cancel or change a transaction, then you should contact by telephone with the MoneyGram branch agent, made the transaction for you. MoneyGram's consumers and agents expect reliability and safety and that is precisely what MoneyGram continues to deliver, transaction by transaction. 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.