Tinea pedia and tinea corporis, which are fungi, cause itching. Clostridia is the bacteria that infects moist open wounds. Gangrene does not itch.
However, itching is often felt when a dry wound is healing. If the gangrene has dried up, and if the open sore has healed and has closed, and there is new skin growing, there may be some itching. The itching may be due to healing skin or it may be due to some tinea corporis on the skin that is healing.
Wash the area of the dry gangrene with some hydrogen peroxide. If white foam or white residue appears in the area, then the application of hydrogen peroxide has just killed the fungi on the skin. If the application of hydrogen peroxide does not produce any white residue, then the itching would be due to the growth of new skin.