There in no way that we can drop that animation down to only 3820 bytes. It might even be difficult to get a good static image in at that size. Now that I look at it, you need the Tink image changed anyway. It's way too wide.
By downsizing your flying tink to fit within the 200 pixel width, it reduced the file size quite a bit too. Here is the one that fits the guidelines. Still the two of them together are too big. I'll see if I can reduce the other's file size some and get them so that together they are under 30K.
Here is the other one. I reduced it by pulling out one frame of the animation. See what you think. As they are right now in this post, I believe the two would fall in the guidelines for signature clipart.