Enhancing the interpretability of AI techniques is paramount for increasing their acceptability, especially in highly interdisciplinary fields such as remote sensing, in which scientists and practitioners with diverse backgrounds work together to monitor the Earth's surface. In this context, counterfactual explanations are an emerging tool to characterize the behaviour of machine learning systems, by providing a posthoc analysis of a given classification model. Focusing on the important task of land cover classification from remote sensing data, we propose a counterfactual explanation approach called CFE4SITS (CounterFactual Explanation for Satellite Image Time Series). One of its distinctive features over existing strategies is the lack of prior assumption on the targeted class for a given counterfactual explanation. This inherent flexibility allows for the automatic discovery of relationship between classes. To assess the quality of the proposed approach, we consider a real-world case study in which we aim to characterize the behavior of a ready-touse land cover classifier. To this end, we compare CFE4SITS to recent time series counterfactual-based strategies and, subsequently, perform an in-depth analysis of its behaviour.