This paper proposes a modified deadlock avoidance method for the TA-Prioritized algorithm by Liu et al. [1]. Their algorithms were developed for the offline Multi-Agent Pickup and Delivery (MAPD) problems where a team of agents have delivery tasks with known release times (when the tasks are ready for pickup.) Offline MAPD problems exist in settings such as warehouses and factories where the release times of tasks are known in advance and Liu et al. [1] make use of this information to compute a good task sequence for each agent using a travelling salesman problem (TSP) solver. The task sequences are then used to plan agent paths accordingly and the deadlock avoidance method proposed attempts holding the pickup locations (keeping an agent stationed at a vertex) if an agent has reached it before the release time and retrying a 1 timestep delayed path from the agent’s initial parking location if any of the agent’s tasks’ path finding fails.