It's not a "conservation of center of mass"$^*$. You just know that the center of mass will not move. This is because we are assuming that the water does not supply any horizontal force to the canoe, so we know that the net external force acting on the woman-canoe system is $0$. This means that $$\mathbf F_\text{ext}=\frac{\text d\mathbf p_\text {total}}{\text dt}=M\frac{\text d\mathbf x_\text {COM}}{\text dt}=0$$
Since the center of mass was not moving before the woman starts walking, this means that it cannot move while the woman is walking also.
$^*$Typically we reserve the word "conserved" for quantities that can be gained or lost by the system, such as energy or momentum. It also suggests that there could be a "flow", i.e. for a closed system of two bodies, they can exchange energy while the total energy of the system is conserved.
Systems don't really "gain" or "lose" center of mass, so it's odd to say that this is "conserved". Additionally, it's not like one object can give "center of mass" to another object. I suppose you could argue in this scenario that center of mass is "conserved", but I think it's somewhat of an odd term for this specific quantity.