When the laser force acts for a short enough time and is strong enough, after the impact the orbiting body will acquire non-negligible positive radial velocity

When the laser force acts for a short enough time and is strong enough, after the impact the orbiting body will acquire non-negligible positive radial velocity while changing its distance from the Earth only negligibly. In the limit of an instantaneous impact, the body will change its velocity in a jump while not moving from the point of impact at all. Then it will continue to orbit the Earth on a new, elliptic orbit that shares with the old circular orbit the point of impact. Since at this point the new radial velocity is positive, the body at this point is getting further away from the Earth. This means that before it will approach the point of impact again, it will have to be nearer the Earth. Hence the perigee is nearer the Earth than the point of impact.