As LLM-based agents are increasingly used in long-term interactions, cumulative memory is critical for enabling personalization and maintaining stylistic consistency. However, most existing systems adopt an "all-or-nothing" approach to memory usage: incorporating all relevant past information can lead to Memory Anchoring, where the agent is trapped by past interactions, while excluding memory entirely results in under-utilization and the loss of important interaction history. We show that an agent’s reliance on memory can be modeled as an explicit and user-controllable dimension. We first introduce a behavioral metric of memory dependence to quantify the influence of past interactions on current outputs. We then propose Steerable Memory Agent, SteeM, a framework that allows users to dynamically regulate memory reliance, ranging from a fresh-start mode that promotes innovation to a high-fidelity mode that closely follows interaction history. Experiments across different scenarios demonstrate that our approach consistently outperforms conventional prompting and rigid memory masking strategies, yielding a more nuanced and effective control for personalized human-agent collaboration.