Expectation inequality of a function with standard normal variable as input

Question

The article "PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming" gives the proof of obtaining the solution for phase retrieval. Here, he used the result
$ \boldsymbol{E}|(z_1^2 -1)1_{z_1^2 \leq 2\beta log(n)} | \leq (2\beta log(n))^{k-2}\boldsymbol{E}(z_1^2 -1)^2 $
Where $\boldsymbol{E} $ is the expectation and $ z_1 \sim \mathcal{N}(0,1)$. $\beta $ is a constant and $n$ is the number of measurements taken which is also constant. It is present in page 19 of the article. How is this inequality obtained? The link to the article https://arxiv.org/pdf/1109.4499.pdf
Edit:The inequality is used in page 19 of the paper