In the last decade, grating-based phase-contrast computed tomography (gbPC-CT) has received growing interest. It provides additional information about the refractive index decrement in the sample. This signal shows an increased soft-tissue contrast. However, the resolution dependence of the signal poses a challenge: its contrast enhancement is overcompensated by the low resolution in low-dose applications such as clinical computed tomography. As a result, the implementation of gbPC-CT is currently tied to a higher dose. To reduce the dose, we introduce the self-supervised deep learning network Noise2Inverse into the field of gbPC-CT. We evaluate the behavior of the Noise2Inverse parameters on the phase-contrast results. Afterward, we compare its results with other denoising methods, namely the Statistical Iterative Reconstruction, Block Matching 3D, and Patchwise Phase Retrieval. In the example of Noise2Inverse, we show that deep learning networks can deliver superior denoising results with respect to the investigated image quality metrics. Their application allows to increase the resolution while maintaining the dose. At higher resolutions, gbPC-CT can naturally deliver higher contrast than conventional absorption-based CT. Therefore, the application of machine learning-based denoisers shifts the dose-normalized image quality in favor of gbPC-CT, bringing it one step closer to medical application.