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{\bf Background processes}  The major background identified in Ref.~\cite{Amjad_2013} (which Ref.~\cite{Baer_2013} is based upon) is the single-top production in association with a W boson and a b quark, through WW$^\ast$ production, as it leads to the same final state as the top-quark pair production. The corresponding cross section~\cite{Boos_2001} increases fast with the centre-of-mass energy, and critically depends on the incoming beam polarization. At $\sqrt{s} = 500$\,GeV (case studied in Ref.~\cite{Baer_2013}), 500$\,GeV,  the single-top production cross section can reach up to 20\% of the top-pair production cross section in the final state with an electron or a positron and in the ${\rm e^-_L e^+_R}$ initial polarization configuration, but this background has yet to be included in the top-quark electroweak coupling study. At $\sqrt{s} = 360$\,GeV and with unpolarized beams, however, the single-top cross section amount to about 0.1\% of the pair production cross section in the same final state, and can therefore be safely ignored wihtout additional uncertainties. {\bf Other experimental uncertainties}