This image was constructed with a gradient-filled circle with the white-filled art on top (no strokes). Then I copied the circle to the top of the layer and applied a clipping mask to trim the edges of the tree to the background. I can't figure out why it looks like a bit of the background circle is showing as a faint line around the artwork. I didn't move anything when copying the circle to make the clipping mask. A clipping mask seemed the easiest way to do this. Should I have used one of the pathfinder tools instead?
It is caused by anti-aliasing as already suggested. However you can avoid it altogether if you change the way the graphic is constructed.
Draw the circle, place the tree graphic on top of the circle
Select both circle and tree graphic, open the path finder and use Minus Front
Select the result and click Path > Compound Path > Make
Apply the gradient, remove any left over stroke.