What type of cloth covers the back of the stage and can be painted?

The correct choice is "C" because a backcloth is specifically designed to be a painted piece of fabric that hangs at the back of the stage, serving as an important visual element in theatrical productions. The ability to paint on this cloth allows for the creation of scenic backgrounds that enhance the storytelling and set the mood of the performance.

Backdrops, while similar, are typically more rigid and may not offer the same flexibility in terms of artistic expression since they often consist of a fixed image or scene. Canvas, on the other hand, refers to the fabric material itself and does not specifically indicate the use within the context of stage design. Gauze is a lightweight fabric often used for special effects or to create a translucent appearance, but it is not typically painted in the same way as backcloths or backdrops. Therefore, the most suitable term for a type of cloth that covers the back of the stage and can be painted is indeed backcloth.