Identify the components of the displacement.

The girl walks 100 m due East and then 100 m due North. These two movements are perpendicular to each other.
Let the eastward displacement be $\Delta x = 100 \text{ m}$.
Let the northward displacement be $\Delta y = 100 \text{ m}$.

The displacement is the straight-line distance from the starting point to the final point, which forms the hypotenuse of a right-angled triangle.
Let $d$ be the magnitude of the displacement.

Using the approximation $\sqrt{2} \approx 1.414$:

The calculated displacement is approximately $141.4 \text{ m}$.
The given options are:
A. 100
B. 150
C. 200
D. 250

The closest option to $141.4 \text{ m}$ is $150 \text{ m}$.

The final answer is $\boxed{\text{B. 150}}$.