On Brendle's estimate for the inscribed radius under mean curvature flow

In a recent paper, Brendle proved that the inscribed radius of closed embedded mean convex hypersurfaces moving by mean curvature flow is at least 1/((1+\delta)H) at all points with H > C(\delta,M_0). In this note, we give a shorter proof of Brendle's estimate, and of a more general result for alpha-Andrews flows, based on our recent estimates from Haslhofer-Kleiner.