You can’t control what’s inside the GIF once it’s made.
So if lettering is blurry or the animation choppy/stuttering it’s most likely a poorly generated GIF animation.
If you’re looking at it on a retina/high res display and the DPI of the image is something like 72 or lower then thats a factor right there. Up it to 144 or more for a better result.
I took a quick look at your site, If you mean the advert below the footer, it looks fine to me. But I’m not sure what you’re expecting ofcourse 🙂 I’m using a Retina display mac.