Low salinity waterflooding (LSW) is an effective method for enhancing the oil recovery from many reservoirs, and its success has been traced to a host of low salinity effects. In this work, we perform molecular dynamics simulations to study the feasibility of recovering oil trapped by nanopores by lowering the reservoir salinity. The oil is initially trapped by a slit nanopore, with a portion of the oil protruding from the pore entrance. After the reservoir salinity is lowered, the thin brine films that separate the oil and pore walls become thicker to drive some of the trapped oil out of the pore. We quantify the free energy profile of this process and clarify the underlying molecular mechanisms. Interestingly, the brine film growth is dominated by the water transport from the brine reservoir into the pore rather than by the depletion of ions from the brine film. These results provide molecular evidence that low salinity brines benefit the recovery of the oil trapped by nanopores. They highlight that when ion depletion from thin brine films is suppressed, the osmosis of water can play a fundamental role in the expansion of the brine films; thus, the enhanced oil recovery. The slow osmosis of water through thin brine films and thus the slow displacement of oil from the pore may help explain the anomalously slow oil recovery reported in micro-modeling experiments of LSW.