Traditionally, recommendation systems are built on the assumption that each service provider has full access to all user data generated on its platform. However, with increasing data privacy concerns and personal data protection regulation, service providers such as Google, Twitter, and Facebook are enabling their users to revisit, erase, and rectify their historical profiles. Future recommendation systems need to be robust to such profile modifications and user-controlled data filtering. In this paper, we explore how recommendation performance may be affected by time-sensitive user data filtering, that is, users choosing to share only recent N days of data. Using the MovieLens dataset as a testbed, we evaluated three widely used collaborative filtering algorithms. Our experiments demonstrate that filtering out historical user data does not significantly affect the overall recommendation performance, but its impact on individual users may vary. These findings challenge the common belief that more data is essential to better performance, and suggest a potential win--win solution for services and end users.