Is a transaction that involves giving a MasterCard to a person to purchase a commodity, with the condition of taking an additional amount (20,0 Iraqi Dinars) for the card service, considered an ijara (leasing/hiring) or a loan that drew benefit?

Giving your Visa card to someone else for them to make purchases, on condition that they repay the amount with an increase, is a prohibited usurious loan (riba), because it is a stipulation for an increase in a loan. There is no difference between giving them the card and you making the purchase for them using the card.

If you desire profit, you have two ways: The first is that you buy the commodity for yourself, then take possession of it, then sell it to him at a profit. The second is that you act as an agent for a fee, whereby he gives you the money first, and you buy the commodity for him in exchange for a known commission.