The sterile males compete with the rest of the population, which drops off the population as mating produces no offspring. This has been attempted with good results in several cases:
Ok, that's how I thought it would work (though "genetically modified" might be the wrong term here, as in those cases sterility comes from direct processes like radiation). I'm astonished that it would be considered feasible given the magnitude of the mosquito population (I'm assuming at least trillions). To cut the mosquito population in half for a generation, you'd need to replace half of the males on the planet, would you not? Or at least make half of the females choose to mate with the modified males.