We present a new Monte Carlo method to estimate the mean-residence time of a diffusive particle in a domain surrounded by a thin layer of low diffusivity. Through a homogenization technique, the layer is identified with a membrane. The simulations use a stochastic process called the snapping out Brownian motion whose density matches the suitable transmission conditions at the membrane. We provide a benchmark test, which is a simplified form of a real-life problem coming from brain imaging techniques. We also refine the ways to estimate the exponential rate of the tail of the distribution function using Monte Carlo simulations.