A quick check suggests grasses live in mangrove forests (Mangals) only in the inland side, so you may need to specify that. It's hard to say whether any non-Spartina (an exotic species), non-submerged (non-"seagrass") grass species live in mangals from a quick check. Submerged seagrass-esque species are surely too specialized for a genus.
However, since the mangals surely experience storm-related flooding, it's possible even the spores or individual flora would be occasionally transported elsewhere. Since there is that tiny Ittiz Temperate Rainforest Archipelago island very conveniently between the Ittiz and and Abello Archipelagos, I did a back-of-the-envelope calculation that the distance is roughly 58.7 miles.
In case you're wondering, I "eyeballed" the distance by comparing the globe map to Google Maps' globe map, picking two states that were small and close together, and making two pins of roughly the distance, which happened to fall in "Harrison Township School District, Harrison Township, New Jersey" and "Cecil County, Maryland".
In all likelihood, there are probably insignificant islets not visible from space in between. As an example of an insignificant islet that could be a stepping stone, Just Room Enough Island in New York's Thousand Islands island chain is only 310 m2, just barely enough room for a house, and it still has some grass.
In short: that vaguely kidney-bean-shaped island is what makes the jump plausible without even a loss in genetic diversity as a penalty. (I've already spent about 30 minutes on this one evaluation, so I think researching the spread of non-coconut plants that float through the ocean would be excessive.)
These are full sun-only, right, and live in soil of moderate to high fertility, right?