Personally, I would call the object in the photograph a "lattice". Wiktionary gives a definition as: "A flat panel constructed with widely-spaced crossed thin strips of wood or other material, commonly used as a garden trellis.".
There is some overlap between the meanings of "grid", "trellis", "grating" and "mesh", but they are used to convey different concepts.
A "grid" describes the partitioning of space or objects into cells. Not sure if the object in the picture does that. A grid is also used to describe barriers made from parallel lines of metal to stop animals passing over. These are usually elongated and do not form square holes. They are more a type of grating.
A "trellis" is defined by its function as a support for plants to grow on. If you were to put your invention in a garden, it would make sense to call it a trellis.
A "grating" is a barrier which allows certain materials to pass through. There is an optical device called a grating. You may want to check if your device is analagous on a larger scale. Gratings seem to be dominant in one direction: main parallel lines with few if any perpendicular lines connecting them.
A "mesh" describes an interwoven configuration of material and is applicable to the object in the image, but "lattice" works better.