Please ignore the answers from the ill informed people who say you'll burn your house down and blow up.
The 20 amp GFCI is not going to cause over-current in your circuit, it just means that particular device is safe for use in applications with up to 20 amps.
Its the breaker that limits how much amperage can flow through that circuit. if you have a 15 amp breaker in good working order and you plug in a device that attempts to pull 20 amps then the GFCI outlet will handle it just fine, but the breaker will trip to protect from overheating the wires.
Heck, you could put in a 200 amp GFCI plug (if such a thing existed) and you'd be fine because your 15 amp breaker would still prevent you from pulling anything more than 15 amps through the wires.
The GFCI outlet does NOT monitor amperage. It monitors how much electricity is going out through the hot side of the circuit and how much is coming back through the neutral. If those don't match, then it means something is escaping to ground (either the ground prong or directly to a connection to the ground). When that happens you have a "ground fault" and the GFCI device will interrupt the circuit. That's why its called a "Ground Fault Circuit Interrupter" - because it interrupts the electrical circuit if there is a fault with electricity flowing to ground.
No amount of amperage will trip a GFCI. Lets say you stick with the 15 amp GFCI, and you plug in some device that pulls 50 amps through your circuit. And lets say your breaker fails and doesn't trip, so electricity just keeps flowing at 50 amps - the GFCI will just let it flow until the components get hotter and hotter and the whole thing melts and burns down the house. But that fire would be due to the faulty breaker and the moron who plugged in a 50 amp device to a standard outlet, not because of your GFCI.