Tau-lepton decays with up to two $pi^0$s in the final state, $tau^+ to pi^+ bar{ u}_tau$, $rho^+ (pi^+pi^0) bar{ u}_tau$, $a^+_1 (pi^+pi^0pi^0) bar{ u}_tau$, are used to study the performance of the barrel part of the silicon-tungsten electromagnetic calorimeter (Si-W ECAL) of the International Large Detector (ILD) at the future $e^+-e^-$ International Linear Collider. A correct reconstruction of the tau decay mode is crucial for constraining the tau spin state and measuring the Higgs boson CP state in $Hto tau^+tau^-$ decays. About 95% of $pi^+ bar{ u}_tau$ and 90% of $rho^+bar{ u}_tau$ and $a^+_1bar{ u}_tau$ decays from $e^+e^-to Z^0to tau^+tau^-$ reaction at $e^pm$-beam energy of 125 GeV are correctly reconstructed. In a smaller ILD detector, with Si-W ECAL radius reduced by about 20% these numbers degrade by at most 2%. The $pi^0$ mass resolution stays below 10%. Since the failures in the tau-lepton reconstruction are mainly due to photons, the increase of the ILD magnetic field from 3.5 T to 4 T does not bring any significant improvement.
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