In grid workflow systems, existing representative checkpoint selection strategies, which are used to select checkpoints for verifying fixed-time constraints at run-time execution stage, often select some unnecessary checkpoints and ignore some necessary ones. Consequently, overall temporal verification efficiency and effectiveness can be severely impacted. In this paper, we propose a new strategy that selects only necessary and sufficient checkpoints dynamically along grid workflow execution. Specifically, we introduce a new concept of minimum time redundancy as a key reference value for checkpoint selection. We also investigate its relationships with fixed-time constraint consistency. Based on these relationships, we present our strategy which can improve overall temporal verification efficiency and effectiveness significantly.