Edge data centers process latency-sensitive workloads of nearby Internet-of-Things devices. These security-critical, multi-tenant environments are equipped with comparatively limited compute resources. Consequently, resource management must be fast and predictable even in the presence of malicious tenants because there is no surplus of resources to compensate for performance attacks. In particular, there is a need to constrain the time it takes to reclaim memory from applications. Existing accounting mechanisms in operating systems focus on limiting memory or scheduling-time usage; they provide no guarantees about the latency of resource reclamation, which can vary greatly and is a potential vector for performance attacks. To solve this standing issue, we introduce BRUMM (Bounded Reclamation of User-space Memory Mappings): This accounting-driven mechanism predicts and tracks how long it will take to reclaim memory allocated to applications, enforcing an upper limit via a configurable latency budget. As a case study, we extended the L4Re microkernel to add a quota object for reclamation latency and enforce its limit. Our evaluation demonstrates that this implementation of BRUMM achieves a consistent overestimation of reclamation latency, staying within the same order of magnitude to real, measured latencies. The implementation only shows modest performance overhead on kernel operations, ranging from 2.4% overhead for simple system calls to 28% in synthetic worst-case scenarios. BRUMM makes reclamation latency a first-class resource that can be accounted for, thereby improving isolation and reliability in edge clouds.