If its actually a unit marker, its probably a maintenance unit. However, It seems suspicious that there is no unit markings, no size, and no unit identifies. For example, this symbol is what I would typically consider to be a unit marker. It is evident, by the information provided around the symbol (as well as symbol itself) that we are looking at the 14th Mechanized Brigade. Your map doesnt include any of this information. Thus, Im suspicious.

Further, lets consider the rest of the map. I cant find any other units, even in the landing zones. Typically, the zones should be capped by a Symbol designating the unit intended to effect that landing. There is none of that. But the map is filled with artillery symbols, and unit numbers for those units. Then you have all that garbage on the beach, which kind of looks like a wall. Finally, there is are those zones, which have lines inside irregular boxes. I think youve mistook one of these for a unit symbol. But, I dont think those are unit symbols at all. Instead, I would think that this is a map of German defenses and artillery units in the area. The red lines along the beach are probably walls and fortified positions, while the cannon looking symbols are batteries. The boxes are hard to identify without proper context, but I would think theyre probably German garrisons, bases, marshalling areas, motor pools, dumps, ect. The number could be number of men, vehicles, buildings under the box, or anything really. Without know for sure what the the box represents, its impossible to say.

But all this is really a shot in the dark without context. If I were you (unsolicited advice inbound) I would try and find out what the map is. Where did you get it? Do you have any other associated paper work? Any similar maps?

I don't have access to any WWII-era field manuals, but the system they used then serves as the basis for what's still used today. Which is to say that it's largely an expansion of what they were doing in WWII, and so a current reference should still contain descriptions for the older symbology.

The current Army Field Manual that details this is FM 1-02, OPERATIONAL TERMS AND GRAPHICS

Chapter 5 details what goes into unit markings. However, I don't think this is a unit marking. Here are my reasons:

1. The rectangle indicates a friendly unit. But it's placement and color would imply that it's unlikely to be friendly.
2. It doesn't quite match any existing unit type indicators:
   • The infantry symbol is a large "X" going from each corner to the opposite corner. The mystery symbol clearly has a horizontal element that the infantry mark doesn't contain.
   • The maintenance symbol is supposed to be a stylized wrench in the center of the box. I can imagine that someone might be sloppy and have the ends of the wrench extend out to the edges of the box, but I can't imagine that someone would repeatedly draw the lines carefully out to each corner. The symbol is clearly deliberate, not lazy.
   • There aren't any size indicators or text containing the names of the units.
   • It's very close to the symbol for "Theater/Echelons Above Corps Support Element". However that mark doesn't have the horizontal center bar on it. The generic mark for a supply unit does include a horizontal line, but it's off-center toward the bottom rather than centered.
3. But most damningly, there's at least one appearance of this symbol that isn't a rectangle. Instead it's clearly a deliberately drawn irregular 4-sided shape. It's in the 6042 grid square on the map, east-southeast of the town. You can also see a very large one in the upper-left hand corner of the map, and another one that gets cut off in the center-top of the map. This implies to me that it's some sort of graphic control measure defining the terrain in some fashion. Some ideas:
   • If the 4 edges of the symbol indicate the perimeter of the terrain being defined, then what's left looks very much like the marker for a lane (i.e. some specific path through an obstacle). This is a long-shot... I don't think this is the answer.
   • It's an indicator of a base or fixed facility of some sort
   • The legend says that the info was provided by the 8th Fleet N-2 - so maybe these are symbols specific to naval usage?

It looks like a military map marking symbol. There are a lot of them and they aren't usually shown on the printed map legend as they are added by hand as intelligence reports unit movements, often on a clear talc overlay so they can be amended. In general form, a rectangle, this appears to be a symbol indicating a friendly unit. Unfortunately it doesn't look quite like any standard symbol.

Generally there are indicators above the symbol to show its hierarchical size, such as squad, company, brigade etc, and numbers beside the symbol (left side) to show the unit designator.

The detail inside the rectangle shows what type of unit is indicated. A diagonal cross touching each corner (bandoliers) indicates infantry. The symbol shown MIGHT be a poorly drawn symbol for an Ordnance unit which is the only symbol showing that ridgeline and the projecting prongs at each end although the prongs should not reach the corners of the frame. It can be thought of as a stylised spanner.

There were a number of Ordnance units on Operation Dragoon. Check if any of the numbers next to those symbols match the unit designators for any of the ordnance units.