It has been suggested that late-universe dark matter decays can alleviate the
tension between measurements of $H_0$ in the local universe and its value
inferred from cosmic microwave background fluctuations. Decaying dark matter
can potentially account for this discrepancy as it reshuffles the energy
density between matter and radiation and as a result allows dark energy to
become dominant at earlier times. We show that the low multipoles amplitude of
the cosmic microwave background anisotropy power spectrum severely constrains
the feasibility of late-time decays as a solution to the $H_0$ tension.