There are a number of gammas created at lower energies (<750 KeV) that are due to excitation of iodine atoms in the sodium iodide detector. It is not essential to understand (or measure the energy or count rates of) these gammas as part of the mass of the neutrons experiment, but students (and TAs) are often curious about the peaks which appear in the spectrum.
The only naturally-occurring stable isotope of iodine is iodine-127. The incident neutrons interact with iodine-127 in one of the following two ways, and subsequently emits gammas.
Energy level diagrams and decays schemes are shown below
Many of the possible emitted gammas appear in the neutron spectra (if you know where to look). Note that peaks due to neutrons interacting with iodine are more prominent when the port is open than when it is closed. Also (though not shown), the intensity of these peaks does not decrease significantly with increasing paraffin blocking material as the gammas are produced inside the detector (which is after any possible shielding); Any decrease in amplitude is due to a decrease in neutron flux.
The 511 keV peak which remains prominent when the port is closed is the portion of that peak due to pair-production from the 2.2 MeV gamma (not pair-production from iodine-128 decay).