THANK YOU very much for very quick abd quite correct reply!!
I just jumped on here with the same qquestion/problem! "Expand the Mesh"... perfect.
I have a nested comp (a trombone players head, arm, hands and instrument) that are looping. I wanted to apply the puppet tool to his body to have that move a little as well, but not as complicated as the "head" comp. However, every time the nested comp moved outside the bounds of frame 1 (where the puppet tool had been applied) there were little artifact outlines of the initial frames shape. Hard to explain, but expanding the mesh to include the whole range of motion removed the artifacts.
In my case, expanding the puppet mesh to 99 still left the border cropping some of my motion. Here's how I fixed it.
1) In the precomp you want to puppet, add a solid that fills the entire viewport.
2) In the main composition, add the puppet pins on the precomp and keyframe your motion.
3) Delete the solid from the precomp.
As far as I can tell, since the pins were set when the mesh needed to include the entire viewport, they still include that area even after the solid is deleted.