That's not a trail left behind by the animation it's the bounding box of the clip - I assume that this animation was imported into the movie? If so then what you're seeing is the dithering pattern as Flash tries to reconcile a "transparent" background on the clip with the background colour of the movie. It happens all the time, here's how to get rid of it...
Go to the Flash colour mixer, choose RGB then change your background colour to the closest colour which is a multiple of 16 (change each of the R,G and B values). So if your original colour was something like 211,111,132 you'd tweak it to become 208,112,128 and the dithering artifacts should vanish.
By the way this only works if your display settings are set to 24 or 32 bit colour - at 16 bit colour they will still be there.