  The recent extremely bright gamma-ray burst (GRB), GRB 230307A from a binary
neutron star merger may offer a good probe for the production of GRB-neutrinos.
Within the constraint from IceCube neutrino non-detection, the limits for key
physical parameters of this burst are extracted in different scenarios
including the fireball, Poynting-flux-dominated (PFD) and hybrid jet. Different
from the former nearby `monsters' and due to its smaller isotropic equivalent
radiated energy ($E_{\gamma,\rm iso}\sim4\times10^{52}$ erg), the constraint
seems loose if non-thermal neutrinos produced from photomeson interactions are
the only consideration. However, a quasi-thermal neutrino emission from
hadronuclear processes is constrained in this neutron-rich post-merger
environment, and the upper limit of the allowed nucleon loading factor is about
a few. Based on this, a discussion is presented on the possible prompt emission
mechanism and jet composition for GRB 230307A in the context of multi-messenger
astrophysics. It is worth noting that till now no GRB-neutrinos have been ever
detected, even for the two brightest nearby GRBs ever observed (GRB 221009A and
GRB 230307A) which have different dissipation mechanisms.
