We present a numerical study on the minimum reflection channel of a disordered waveguide and its modification by coherent amplification of light. The minimum reflection channel is formed by destructive interference of quasi-normal modes at the front surface of a random medium. While the lowest reflection eigenvalue increases with optical gain in most random realizations, the minimum reflection channel can adjust its modal composition to enhance destructive interference and slow down the growth of reflectance with gain. Some of the random realizations display a further reduction of the minimum reflectance by adding optical gain. The differential amplification of the modes can make their destructive interference so effective that it dominates the amplitude growth of the modes, causes the reflectance to drop with gain in these cases. Therefore, the interplay between interference and amplification can further minimize light reflection from a strong scattering medium; indicating optical gain may provide an additional degree of freedom for coherent control of mesoscopic transport.