  The renormalization of the $T$-matrix for $NN$ scattering with a contact
potential is reexamined in a nonperturbative regime through rigorous
nonperturbative solutions. Based on the underlying theory point of view, it is
shown that the UV divergences in the nonperturbative solutions of the
$T$-matrix should be subtracted through 'endogenous' counter terms, which in
turn leads to a nontrivial prescription dependence. Moreover, employing the
effective range expansion, the important procedure for imposing physical
boundary conditions to remove the nontrivial prescription dependence is
discussed and highlighted, especially before making physical claims. As
byproducts, some relations between the effective range expansion parameters are
derived. We also discussed the power counting of the couplings for the
nucleon-nucleon interactions and other subtle points present within EFT
framework beyond perturbative treatment.
