The wave doesn't climb the wall — inside it, |ψ| doesn't oscillate, it decays exponentially (e−κx). A finite wall still has a non-zero amplitude on the far side, so the packet re-emerges — smaller — and keeps going.
That exponent is ferociously sensitive. Widen the gap of a scanning tunneling microscope by a single atom and the current drops about tenfold — which is how an STM feels out one atom at a time.
Gamow explained alpha decay this way in 1928: a factor of two in a nucleus's energy swings its half-life by roughly 1024, from microseconds to longer than the age of the universe.
And the Sun shines only because protons tunnel a barrier some 400× their thermal energy. Without tunneling, the stars would not burn.
Something in the simulation stopped unexpectedly — the lesson continues without it. Nothing you did was wrong; you can move on.