Contact operators in renormalization of attractive singular potentials

We discuss renormalization of chiral nuclear forces in the $^{3}P_{0}$ channel of $NN$ scattering at next-to-next-to leading order (${\mathrm{N}}^{2}\mathrm{LO}$) if the one-pion exchange is treated nonperturbatively at leading order. The matrix elements of the subleading contact potentials become nearly dependent for the so-called exceptional ultraviolet momentum cutoff, making it difficult to determine the strengths of those contact potentials from the empirical phase shifts, as reported by A. M. Gasparyan and E. Epelbaum [Phys. Rev. C 107, 034001 (2023)]. We argue that this issue can be resolved by adjusting the strategy by which the low-energy constants are deduced from the data, thus making those exceptional cutoffs amenable to chiral effective field theory.