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Most upcoming CMB experiments are planning to deploy between a few thousand and a few hundred thousand TES bolometers in order to drastically increase sensitivity and unveil the B-mode signal. Differential systematic effects and $1/f$ noise are two of the challenges that need to be overcome in order to achieve this result. In recent years, rotating Half-Wave Plates have become increasingly more popular as a solution to mitigate these effects, especially for those experiments that are targeting the largest angular scales. However, other effects may appear when a rotating HWP is being employed. In this paper we focus on HWP synchronous signals, which are due to intensity to polarization leakage induced by a rotating cryogenic multi-layer sapphire HWP employed as the first optical element of the telescope system. We use LiteBIRD LFT as a case study and we analyze the interaction between these spurious signals and TES bolometers, to determine whether this signal can contaminate the bolometer response. We present the results of simulations for a few different TES model assumptions and different spurious signal amplitudes. Modelling these effects is fundamental to find what leakage level can be tolerated and minimize non-linearity effects of the bolometer response.