Sharp bounds in Ionescu--Wainger multiplier theorem for canonical fractions

In this short note, we show that the loss of order $N^{c_p\mathrm{/}\log \log N}$ in the version of the Ionescu–Wainger multiplier theorem for canonical fractions, recently established by Kosz, Mirek, Słomian, and Zhang in arXiv:2606.12663, is optimal.