Attention is drawn to some circumstances that were not quite clearly described in the paper by Soares et al. (Eur Phys J Plus 136:966, 2021) and its previous comment by Amore and Fernandez (Eur Phys J Plus, 2024, this issue), in particular, that the Klein-Gordon field under consideration has a discrete spectrum of positive energy states, hard to be found analytically but approaching the spectrum of a usual quantum oscillator at high levels (n >> 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \gg 1$$\end{document}). Corrections to the oscillator spectrum are here calculated in the WKB approximation.