  We investigate the effects of diamagnetic doping in the solid-solution series
$Tb_{1-x}Y_{x}(HCO_{2})_{3}$, in which the parent $Tb(HCO_{2})_{3}$ phase has
previously been shown to host a combination of frustrated and 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 < 0.4 K appears with increasing x. The origin of this unusual behaviour is
rationalised in terms of the fragmentation of quasi-1D spin chains by the
diamagnetic $Y^{3+}$ dopant. Magnetocaloric measurements show a nonlinear
dependence on x. The mass-weighted magnetocaloric entropy decreases across the
series from the promising values in $Tb(HCO_{2})_{3}$; however, the
magnetocaloric entropy per magnetic $Tb^{3+}$ ion first decreases then
increases with increasing x. Our results establish $Tb_{1-x}Y_{x}(HCO_{2})_{3}$
as a model system in which to explore the functional ramifications of dilution
in a low-dimensional magnet.
