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Loco-manipulation, which requires mobile manipulators to coordinate locomotion and manipulation over long horizons, is a key capability for large-object rearrangement in applications such as service robotics and warehouse automation. Despite recent progress, reliably executing these tasks remains challenging because performance depends on complex robot-object and object-environment interaction dynamics. Existing approaches address this challenge either through model-based methods, which often require accurate dynamics models, or through learning-based methods, which reduce this requirement but typically assume a fixed or predefined initial grasp. However, different geometrically stable grasps can lead to substantially different downstream manipulation performance. Therefore, we propose Grasp-TAGS, a task-aware grasp selection framework for goal-conditioned large-object rearrangement. We train a unified PPO-based reinforcement learning policy across multiple initial grasp configurations and distill the learned critic into a lightweight grasp utility network that ranks candidate grasps using only the candidate grasp configuration and goal information. At inference time, we select the grasp with the highest predicted downstream utility for the downstream policy to complete the task, before even making a contact. Experiments demonstrate that Grasp-TAGS improves rearrangement success over both fixed single-grasp policies and random grasp selection, achieving an average success rate of 89.84% compared with 79.87% for the best-performing single-grasp policies, an improvement of 9.97 percentage points. Grasp-TAGS also reduces final orientation errors across all evaluated objects. For more qualitative results, refer to the supplementary webpage: https://rpm-lab-umn.github.io/Grasp-TAGS-web-page/