A well-known result in general relativity is that the tidal Love numbers of black holes vanish. In contrast, different configurations of a black hole may have non-vanishing Love numbers. For instance, it has been conjectured recently that the Love number of generic exotic compact objects (ECOs) shows a logarithmic behaviour. Here, we analyse the ultracompact Schwarzschild star, which allows the compactness to cross and go beyond the Buchdahl limit. This Schwarzschild star has been shown to be a good black hole mimicker. Moreover, it has been found that the Love number of these objects approaches zero as their compactness approaches the black hole limit. Here, we complement those results by showing that the Love number for these configurations follows an exponentially decaying behaviour rather than the logarithmic behaviour proposed for generic ECOs.