We investigate an attack on a machine learning model that predicts whether a person or household will relocate in the next two years, i.e., a propensity-to-move classifier. The attack assumes that the attacker can query the model to obtain predictions and that the marginal distribution of the data on which the model was trained is publicly available. The attack also assumes that the attacker has obtained the values of non-sensitive attributes for a certain number of target individuals. The objective of the attack is to infer the values of sensitive attributes for these target individuals. We explore how replacing the original data with synthetic data when training the model impacts how successfully the attacker can infer sensitive attributes.\footnote{Original paper published at PSD 2022. The paper was subsequently updated.}