Modern search and recommendation systems are optimized using logged interaction data. There is increasing societal pressure to enable users of such systems to have some of their data deleted from those systems. This paper focuses on ‘unlearning’ such user data from neighborhood-based recommendation models on sparse, high-dimensional datasets, via a fast and exact method for deleting interactions from a custom top-k index. We experimentally find that our method provides competitive index building times, makes sub-second unlearning possible (even for a large index built from 1 million users and 255 million interactions), and, when integrated into three state-of-the-art next-basket recommendation models, allows users to effectively adjust their predictions to remove sensitive items. Furthermore, an implementation is shared with this paper.