The use of composite materials to strengthen masonry structures has become common practice within the civil engineering community. Steel-reinforced grout (SRG), which comprises high-strength steel fibers embedded in a mortar matrix, is part of the family of the fiber-reinforced cementitious matrix (FRCM) composites that represent a suitable alternative to fiber-reinforced polymer (FRP) composites for strengthening existing structures. Although studies on FRCMs have already reached a certain level of maturity, some key issues remain open, such as the role of matrix type and layout, substrate properties, and test rate. This paper focuses on some of these issues. The results of single-lap direct shear tests on masonry blocks strengthened with SRGs are presented to analyze the bond behavior between the composite material and the substrate. Four aspects are considered: (1) the change in the width of the SRG mortar matrix while keeping the width of the fiber sheet fixed; (2) the type of mortar used for the SRG; (3) the influence of the test rate, and (4) the type of substrate (i.e., concrete vs. masonry). The results obtained indicate the active role of the matrix layout and the importance of the test rate, encouraging further investigations to clarify these aspects.