Yeah what Fatality said, .gifs should be used only for lineart, if you want to save something in a .gif format, try to use the least possible colors. If you have pictures with alot of colors use jpegs, if you want transparency use pngs,
Your new sig looks grainy because its a gif, gifs only support (if I am right) 256 colors, so save it as .png and it will look a whole lot better. And you really need a new image, the one you use now looks way to blurry and the cutting isnt to great either. I dont know what program you use, but if you ever find low quality pictures and you use photoshop, first make a new layer, past the picture on that layer, duplicate that layer,do a Guassian blur 2.0 on the new layer, and set the blending mode on hard light or softlight depends on what you prefer.