Oh that's wrong way of making images for background or anything
First of all, don't use dithering at all.
2nd use your own palette or to be specific, use image's palette.
For background, you only need to set your image from RGB to indexed color. To ensure first color in palette is transparent color, set that color as forced color.
If you are using Photoshop it's easy for me to show how to force that color.