The goal of Domain Generation Algorithm (DGA) detection is to recognize infections with bot malware and is often done with help of Machine Learning approaches that classify non-resolving Domain Name System (DNS) traffic and are trained on possibly sensitive data. In parallel, the rise of privacy research in the Machine Learning world leads to privacy-preserving measures that are tightly coupled with a deep learning model's architecture or training routine, while non deep learning approaches are commonly better suited for the application of privacy-enhancing methods outside the actual classification module. In this work, we aim to measure the privacy capability of the feature extractor of feature-based DGA detector FANCI (Feature-based Automated Nxdomain Classification and Intelligence). Our goal is to assess whether a data-rich adversary can learn an inverse mapping of FANCI's feature extractor and thereby reconstruct domain names from feature vectors. Attack success would pose a privacy threat to sharing FANCI's feature representation, while the opposite would enable this representation to be shared without privacy concerns. Using three real-world data sets, we train a recurrent Machine Learning model on the reconstruction task. Our approaches result in poor reconstruction performance and we attempt to back our findings with a mathematical review of the feature extraction process. We thus reckon that sharing FANCI's feature representation does not constitute a considerable privacy leakage.