  The recent rapid growth of the black hole (BH) catalog from gravitational
waves (GWs), has allowed us to study the substructure of black hole mass
function (BHMF) beyond the simplest Power-Law distribution. However, the BH
masses inferred from binary BH merger events, may be systematically
'brightened' or 'dimmed' by the gravitational lensing effect. In this work, we
investigate the impact of gravitational lensing on the BHMF inference
considering the detection of the third-generation GW detector -- the Einstein
Telescope (ET). We focus on high redshift, $z=10$, in order to obtain the upper
limits of this effect. We use Monte Carlo (MC) method to simulate the data
adopting 3 original BHMFs under Un-Lensed and Lensed scenarios, then recover
the parameters of BHMFs from the mock data, and compare the difference of
results, respectively. We found that all the parameters are well recovered
within one standard deviation(std., 1$\sigma$), and all 3 BHMF models are
reconstructed within 68\% credible interval, suggesting that lensing would not
change the main structure drastically, even at very high redshifts and with
high precision of ET. And the modest influence beyond $50M_{\odot}$, depends on
the modeling of the high mass tail or substructure of BHMF. We conclude that
the impact of lensing on BHMF inference with ET can be safely ignored in the
foreseeable future. Careful handling of lensing effects is required only when
focusing on an accurate estimation of the high mass end of BHMF at high
redshifts.
