Resettlement agencies have started to adopt data-driven algorithmic matching to match refugees to locations using employment rate as a measure of utility. Given a pool of refugees, data-driven algorithmic matching utilizes a classifier to predict the probability that each refugee would find employment at any given location. Then, it uses the predicted probabilities to estimate the expected utility of all possible placement decisions. Finally, it finds the placement decisions that maximize the predicted utility by solving a maximum weight bipartite matching problem. In this work, we argue that, using existing solutions, there may be pools of refugees for which data-driven algorithmic matching is (counterfactually) harmful -- it would have achieved lower utility than a given default policy used in the past, had it been used. Then, we develop a post-processing algorithm that, given placement decisions made by a default policy on a pool of refugees and their employment outcomes, solves an inverse~matching problem to minimally modify the predictions made by a given classifier. Under these modified predictions, the optimal matching policy that maximizes predicted utility on the pool is guaranteed to be not harmful. Further, we introduce a Transformer model that, given placement decisions made by a default policy on multiple pools of refugees and their employment outcomes, learns to modify the predictions made by a classifier so that the optimal matching policy that maximizes predicted utility under the modified predictions on an unseen pool of refugees is less likely to be harmful than under the original predictions. Experiments on simulated resettlement processes using synthetic refugee data created from a variety of publicly available data suggest that our methodology may be effective in making algorithmic placement decisions that are less likely to be harmful than existing solutions.