Face recognition systems rely on learning highly discriminative and compact identity clusters to enable accurate retrieval. However, as with other surveillance-oriented technologies, such systems raise serious privacy concerns due to their potential for unauthorized identity tracking. While several works have explored machine unlearning as a means of privacy protection, their applicability to face retrieval - especially for modern embedding-based recognition models - remains largely unexplored. In this work, we study the problem of face identity unlearning for retrieval systems and present its inherent challenges. The goal is to make selected identities unretrievable by dispersing their embeddings on the hypersphere and preventing the formation of compact identity clusters that enable re-identification in the gallery. The primary challenge is to achieve this forgetting effect while preserving the discriminative structure of the embedding space and the retrieval performance of the model for the remaining identities. To address this, we evaluate several existing approximate class unlearning methods (e.g., Random Labeling, Gradient Ascent, Boundary Unlearning, and other recent approaches) in the context of face retrieval and propose a simple yet effective dispersion-based unlearning approach. Extensive experiments on standard benchmarks (VGGFace2, CelebA) demonstrate that our method achieves superior forgetting behavior while preserving retrieval utility.