Detecting causality in coupled nonlinear dynamical systems is challenging for the classic Granger Causality (GC) paradigm due to mirage correlations arising from coupling effects. Convergent Cross Mapping (CCM) was introduced as a model-free alternative to complement GC in such scenarios, yet its performance can deteriorate considerably in the presence of noise. Many studies on cross-mapping-based causal discovery assess their models using only noise-free or minimally noised simulated systems, overlooking real-world data that are often susceptible to significant noise. To address this gap, we examine the noise sensitivity of CCM and demonstrate how simple preprocessing with averaging filter can enhance its robustness. Through experiments on the noisy Lorenz system and the realworld weather dataset ERA5, we provide insights into filter parameter selection and its impact on inference quality, offering practical guidance for noisy causal inference in nonlinear systems. Additionally, we hypothesize that in the context of the systems we study, causal information may reside predominantly in lower-frequency domains, explaining why averaging filters-by removing high-frequency noise-improve causal inference.