During deuterium-only neutral beam injected discharges, tritium from earlier deuterium-tritium (DT) discharges is released from the vessel limiters and walls to cause a DT neutron count rate comparable to the DD neutron count rate. A measure of the tritium density in the plasma based on neutron rate measurements is defined and used to determine which parameters influence tritium influx to the plasma core. The tritium density is observed to decrease in a sequence of deuterium-only supershots and to depend on the amount of tritium injected in prior DT shots and on the amount of tritium present in the limiter. A weak correlation is also observed with the plasma current, but not with beam power, hydrogen influx, carbon influx, visible bremsstrahlung, lithium pellet injection, blooms or disruptions