Do you want to delete the animation or the static logo?

Uploading a blank logo should work to get rid of the static logo, or using the Logoedit delete feature as Paul suggested.

However, the final frame of the animation will hang around on the screen if there is no static logo. To get rid of that, you must edit the animation using Jemplode. There's no way to delete the animation, the only way to change it is to upload a blank animation.