We have studied laser induced material modication in a frequency tripling mirror (FTM) consisting of alternating hafnia and silica layers. The third-harmonic signal generated by a train of femtosecond laser pulses (791 nm, 55 fs, 110 MHz) drops over time until it reaches about 20\% of the initial value. From the observed changes in reection and transmission of the mirror a refractive index change of 0:07 was estimated, which occurs in the layer with the highest eld enhancement. This index change triggers a drop in the eld enhancement, which reduces the eciency of nonlinear optical processes. The estimated value of n allowed us to explain the 80\% reduction in conversion eciency and as well as an observed decrease in two-photon absorption.