If you need it to be removed from the world upon a click, you can call
if (Greenfoot.mouseClicked(this)) {
getWorld().removeObject(this);
}
wherever you need to check for it. However, you need to make sure you don't try to access anything about the world (location, which world the actor is in) after the button is deleted, or else you can get some exceptions. But the solution I provided should cover most situations. If you have trouble, please respond back.