  Identifying strong lensing gravitational wave (SLGW) events is of utmost
importance in astrophysics as we approach the historic first detection of SLGW
amidst the growing number of gravitational wave (GW) events. Currently, one
crucial method for identifying SLGW signals involves assessing the overlap of
parameters between two GWs. However, the distribution of discrete matter, such
as stars and sub-halos, within the strong lensing galaxy can imprint a wave
optical (WO) effect on the SLGW waveform. These frequency dependent imprints
introduce biases in parameter estimation and impact SLGW identification. In
this study, we assess the influence of the stellar microlensing field embedded
in a strong lensing galaxy. Our finding demonstrate that the WO effect reduces
the detection efficiency of SLGW by $5\%\sim 50\%$ for various false alarm
probabilities per pair (${\rm FAP}_{\rm per~pair}$). Specifically, at an ${\rm
FAP}_{\rm per~pair}$ of $10^{-5}$, the detection efficiency decreases from
$\sim 10\%$ to $\sim 5\%$. Consequently, the presence of the microlensing field
can result in missing half of the strong lensing candidates. Additionally, the
microlensing WO effect introduces a noticeable bias in intrinsic parameters,
particularly for chirp mass and mass ratio. However, it has tiny influence on
extrinsic parameters. Considering all parameters, $\sim 30\%$ of events exhibit
a $1\sigma$ parameter bias, $\sim 12\%$ exhibit a $2\sigma$ parameter bias, and
$\sim 5\%$ exhibit a $3\sigma$ parameter bias.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology