PURPOSE: Breast cancer is the most common malignancy in women. Unfortunately, current breast imaging techniques all suffer from certain limitations: they are either not fully three dimensional, have an insufficient resolution or low soft-tissue contrast. Grating interferometry breast computed tomography (GI-BCT) is a promising X-ray phase contrast modality that could overcome these limitations by offering high soft-tissue contrast and excellent three-dimensional resolution. To enable the transition of this technology to clinical practice, dedicated data-processing algorithms must be developed in order to effectively retrieve the signals of interest from the measured raw data. METHODS: This article proposes a novel denoising algorithm that can cope with the high-noise amplitudes and heteroscedasticity which arise in GI-BCT when operated in a low-dose regime to effectively regularize the ill-conditioned GI-BCT inverse problem. We present a data-driven algorithm called INSIDEnet, which combines different ideas such as multiscale image processing, transform-domain filtering, transform learning, and explicit orthogonality to build an Interpretable NonexpanSIve Data-Efficient network (INSIDEnet). RESULTS: We apply the method to simulated breast phantom datasets and to real data acquired on a GI-BCT prototype and show that the proposed algorithm outperforms traditional state-of-the-art filters and is competitive with deep neural networks. The strong inductive bias given by the proposed model's architecture allows to reliably train the algorithm with very limited data while providing high model interpretability, thus offering a great advantage over classical convolutional neural networks (CNNs). CONCLUSIONS: The proposed INSIDEnet is highly data-efficient, interpretable, and outperforms state-of-the-art CNNs when trained on very limited training data. We expect the proposed method to become an important tool as part of a dedicated plug-and-play GI-BCT reconstruction framework, needed to translate this promising technology to the clinics.