The bond behavior of FRCM systems is typically assessed through single-lap shear tests (SSTs), where a parallelepiped-shaped composite specimen is adhered to a substrate, and the textile is pulled out. While these tests effectively evaluate the textile-matrix interaction, they generally overlook the role of the substrate, making the textile-matrix bond the primary response mechanism. Alternatively, pull-out tests are employed to investigate the bond capacity between a reinforcing textile and an embedding matrix. These tests are conducted in either a pull-pull or push-pull configuration, most commonly using cylinder-shaped specimens for the matrix. However, some studies have also explored parallelepiped-shaped samples. Despite the widespread use of these testing methods, a key distinction exists between yarn-matrix and textile-matrix bond behavior. Factors such as transverse yarns, knot effectiveness, and stress inhomogeneities significantly influence the textile-matrix interaction, yet research addressing these complexities remains limited. This study examines an FRCM system composed of fiberglass open textiles embedded in a lime matrix using pull-out tests. Initially, the standalone constituents were characterized to establish their mechanical properties. Subsequently, pull-out tests were performed on individual yarns using the pull-pull configuration with parallelepiped-shaped specimens. To further explore the textile’s behavior, additional tests were conducted on parallelepiped-shaped specimens under the same configuration, and single-lap shear tests were performed as well. A uniform bonded length was maintained across all tests to ensure consistency and comparability of results. Finally, back calibration of the cohesive material law and global stress-slip diagrams estimation have been implemented and compared through a simple analytical model to analyze the experimental findings of the different test setups.