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In this paper, we explore how to use a small amount of new data to update a task-oriented semantic parsing model when the desired output for some examples has changed. When making updates in this way, one potential problem that arises is the presence of conflicting data, or out-of-date labels in the original training set. To evaluate the impact of this understudied problem, we propose an experimental setup for simulating changes to a neural semantic parser. We show that the presence of conflicting data greatly hinders learning of an update, then explore several methods to mitigate its effect. Our multi-task and data selection methods lead to large improvements in model accuracy compared to a naive data-mixing strategy, and our best method closes 86% of the accuracy gap between this baseline and an oracle upper bound.