By default, Ability shows transparent areas of an image as a pattern of grey or white squares. This is to distinguish a blank or transparent area from, for example, an area filled with white color. To control the display of the grid, select Options from the Tools menu and then Grid:
Grid Size – the size of the squares in the grid pattern
Grid Color – dark, light, medium
To turn off the display of the grid pattern, set Grid Size to none (and probably best to set Grid Color to light).