So, the accusation is that Gretna police were keeping blacks from flooding into Algiers?
If you consider allegations from the NAACP to be credible that is the accusation.
The Mississippi River bridge from downtown N.O. (Crescent City Connection) crosses to Algiers, also a part of Orleans Parish. The bridge connects with an elevated expressway that sweeps to the right and parallels the river upstream. There are off-ramps that lead down into Algiers, then you cross into Jefferson Parish. There are off-ramps there that lead into Terrytown, then Gretna and other points down the road.
Gretna is an incorporated city in Jefferson Parish. Their police have no jurisdiction in unincorporated Jefferson Parish or in Orleans Parish (Algiers). IIRC, they closed the elevated roadway (not the "bridge") at the city's incorporation limit line. People crossing the bridge were able to exit the elevated roadway into Algiers and Terrytown, the Gretna PD had no reason to prevent that.