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Interpreting and reconstructing distant sources that are gravitationally lensed by galaxy clusters requires accurate and precise lens models. While high-quality data sets have reduced statistical errors in such models, systematic errors remain important. We examine systematic lensing effects caused by density fluctuations due to large-scale structure along the line of sight. We use a multiplane ray-tracing algorithm with the IllustrisTNG 100-3 cosmological simulation of matter distribution and compute the statistical distributions of shear, convergence, and higher-order deflections using two Hubble Frontier Field clusters as examples (A2744 and MACS J0416.1−2403). The cosmic shear distribution is Gaussian in each component, while the cosmic convergence distribution is skewed such that 1 +κ is consistent with a log-normal distribution; the standard deviations for these quantities are at the level of a few to 10%, depending on the redshift of the source. The deflection from higher-order terms beyond convergence and shear has significant scatter: the rms deflection is ∼15″, considerably larger than the image position residuals for current lens models. These results indicate that line-of-sight deflection effects due to largescale structure can significantly impact lens models and should not be neglected. We present results in forms that can be incorporated into future cluster lens models.