Knowledge of the tensile behaviour of the strengthening material is important to estimate the shear capacity of the strengthened structure. In this paper, the tensile behaviour of externally bonded carbon fibre polymer (CFRP) grids has been studied. Bonding agent was either quasi-brittle polymer-modified mortar (PMM) or strain-hardening (“ductile”) mortar, instead of the typical epoxy resin. Uniaxial tensile and wedge-splitting tests were conducted to investigate the tensile-, and post-cracking behaviour, toughness, and ductility. The strain-hardening mortar enhanced both the load bearing- and in particular, the deformation capacity, surpassing the benefits of the PMM. The “ductile” mortar has also shifted the overall behaviour from brittle towards a more ductile failure.