Hide parts of image in OpenGL ES

I'm using GLKView to render some sprites in a iOS app.

My question is, how can I remove/draw only parts of one image? For example, I have a background, and on top of it an image (both sprites). I want to take some random rectangles out of the image on top, so the background will be visible in those rectangles. Is that possible?

I'm creating my textures like this:

   - (id)initWithFile:(NSString *)fileName effect:(GLKBaseEffect *)effect position:(GLKVector2)position{
    if ((self = [super init])) {
        self.effect = effect;

        NSDictionary * options = [NSDictionary dictionaryWithObjectsAndKeys:
                                  [NSNumber numberWithBool:YES],
                                  GLKTextureLoaderOriginBottomLeft, 
                                  nil];

        NSError * error;    
        NSString *path = [[NSBundle mainBundle] pathForResource:fileName ofType:nil];
        self.textureInfo = [GLKTextureLoader textureWithContentsOfFile:path options:options error:&error];


        self.contentSize = CGSizeMake(self.textureInfo.width, self.textureInfo.height);


        TexturedQuad newQuad;
        newQuad.bl.geometryVertex = CGPointMake(0, 0);
        newQuad.br.geometryVertex = CGPointMake(self.textureInfo.width, 0);
        newQuad.tl.geometryVertex = CGPointMake(0, self.textureInfo.height);
        newQuad.tr.geometryVertex = CGPointMake(self.textureInfo.width, self.textureInfo.height);

        newQuad.bl.textureVertex = CGPointMake(0, 0);
        newQuad.br.textureVertex = CGPointMake(1, 0);
        newQuad.tl.textureVertex = CGPointMake(0, 1);
        newQuad.tr.textureVertex = CGPointMake(1, 1);
        self.quad = newQuad;


        self.position = position;

        self.frameHeight = self.textureInfo.height;

    }
    return self;
}

And then render them like this

- (void)render { 

    self.effect.texture2d0.name = self.textureInfo.name;
    self.effect.texture2d0.enabled = YES;        

    self.effect.transform.modelviewMatrix = self.modelMatrix;

    [self.effect prepareToDraw];

    long offset = (long)&_quad;

    glEnableVertexAttribArray(GLKVertexAttribPosition);
    glEnableVertexAttribArray(GLKVertexAttribTexCoord0);

    glVertexAttribPointer(GLKVertexAttribPosition, 2, GL_FLOAT, GL_FALSE, sizeof(TexturedVertex), (void *) (offset + offsetof(TexturedVertex, geometryVertex)));
    glVertexAttribPointer(GLKVertexAttribTexCoord0, 2, GL_FLOAT, GL_FALSE, sizeof(TexturedVertex), (void *) (offset + offsetof(TexturedVertex, textureVertex)));

    glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);

}

Typically this is done with a second texture that is an alpha map. In the shader, the alpha texture will have regions that are full opaque and other regions that are fully transparent. The alpha channel of the alpha texture is multiplied by the image texture alpha to get the final color.