Satellite telemetry data consists of information transmitted from spacecraft providing their location, status, health and the functioning of the instruments. Due to the data volume, signal quality issues, resolution and orbital constraints, detecting anomalies in satellite telemetry data is challenging. One of the main challenges concerned with the existing methods is the large number of false alarms, contributing to a waste of operational resources and decreased trust in the system. In this paper, we tackle this issue and present Morphological Leave-One-Out Kernel Density Estimates (Mo-LOO-KDE)—an unsupervised anomaly detection method tailored for satellite telemetry data. It combines Extreme Value Theory, a statistical framework for modeling extremes, with computer-vision morphological operations. Here, Extreme Value Theory is used to model rare, extreme events, whereas morphological operations are effectively used for noise reduction. The unusual combination of Extreme Value Theory and morphological operations drive Mo-LOO-KDE’s low false positive rate. The proposed morphological filtering method has no formal requirement for regular sampling, so the method is applicable for irregular time series as well. Furthermore, the employment of a lightweight, unsupervised method such as Mo-LOO-KDE is advantageous due to its practical utility, as annotated and representative ground-truth datasets are expensive to generate and rarely available. Utilizing the 42-month telemetry dataset from the ESA-ADB benchmark, we perform a comparison with the SOTA approach and show that Mo-LOO-KDE outperforms other unsupervised methods, demonstrating its applicability for satellite telemetry.