Textile Reinforced Mortar (TRM) composite systems are gaining consensus within the scientific and technical communities as a viable and advantageous alternative to the most conventional Fibre-Reinforced Polymer (FRP) composites. Due to the good compatibility both in terms of stiffness and vapor permeability between the inorganic matrix and the substrate, the TRMs appear to be particularly well suited for strengthening masonry members and enhancing their capacity to withstand tensile and shear stresses, such as those induced by seismic shakings. This paper aims to investigate the mechanical response of a TRM system featuring an internal reinforcement made of basalt fiber textile. Therefore, the paper reports the results of an experimental campaign carried out by single-lap shear bond tests on masonry substrate reinforced by TRM strips. Three different kinds of TRM have been taken into account, each one characterized by a variable number of fabric plies. The results show that, in all cases, TRMs fail prematurely due to debonding between fabric and matrix. However, the aforementioned premature failure is the main concern emerging from these test results, and further work is requested in reformulating the matrix composition towards enhancing their tensile strength and, hence, restraining the occurrence of fabric-to-matrix debonding.