  Recently, Bueno, Cano, and Hennigar [arXiv:2403.04827] proposed a generic
approach for incorporating an infinite tower of higher-curvature corrections
into the Einstein theory. In this study, we compute quasinormal modes for
certain regular D-dimensional black holes resulting from this infinite series
of higher-curvature corrections, specifically focusing on the $D$-dimensional
extensions of the Bardeen and Hayward black holes. We demonstrate that while
the fundamental mode is minimally affected by moderate coupling constants, the
higher overtones exhibit significant sensitivity even to small coupling values,
yielding unconventional modes characterized by vanishing real oscillation
frequencies. When comparing the frequencies derived from the metric truncated
at several orders of higher-curvature corrections with those resulting from the
infinite series of terms, we observe a rapid convergence of the frequencies to
their limit for the complete regular black hole. This validates the extensive
research conducted on specific theories with a finite number of
higher-curvature corrections, such as the Lovelock theory.
