Quantitative phase imaging (QPI) is an emerging label-free biomedical imaging modality. However, achieving high-fidelity QPI through an optical multicore fiber remains challenging. We demonstrate a novel phase reconstruction algorithm tailored for QPI through a lensless multi-core fiber (MCF) with a diameter of less than half a millimeter. Furthermore, precise reconstruction of the complex light field enables digital refocusing, providing flexible working distance for the lensless endoscope. Moreover, a total variation model is implemented to reduce the noise in the reconstructed images, enhancing the endoscopic image quality. This powerful ultra-thin QPI probe could open new perspectives for endoscopic imaging.