We investigate the effects of diamagnetic doping in the solid-solution series Tb1−xYx(HCO2)3, in which the parent Tb(HCO2)3 phase has previously been shown to host a combination of frustrated and quasi-one-dimensional (quasi-1D) physics, giving rise to a triangular Ising antiferromagnetic ground state that lacks long range 3D order. Heat capacity measurements show three key features: (i) a low temperature Schottky anomaly is observed, which is constant as a function of x; (ii) the transition temperature and associated entropy change are both surprisingly robust to diamagnetic doping; and (iii) an additional contribution at T