In the intermediate depth Eastern Tropical Pacific Ocean, multiple deglacial radiocarbon (14C) records show anomalously low 14C/C values that appear to be best explained by the addition of 14C-free geologic carbon. We use inverse carbon cycle modeling and data assimilation of reconstructed atmospheric CO2 and ∆14C to develop an upper bound constraint on this speculated deglacial geologic carbon release. Our analysis suggests two primary opportunities where large bicarbonate pulses (up to 1.3 PgC yr-1) could occur with little effect on atmospheric CO2 and without upsetting 14C mass-balance constraints. Including the release of 14C-free permafrost carbon and regrowth of the terrestrial biosphere, we obtain a set of permissible scenarios for ocean geologic carbon release that ranges from 900-2400 PgC. Based on these results, we conclude that geologic carbon release is a plausible interpretation for the spatio-temporal cluster of anomalous 14C data near the East Pacific Rise.