This handy little tool is one of my favorite things. It's a brush called a Colour Shaper, that has a solid rubber-like material instead of bristles on the end. It comes in different sizes and shapes, and it's my secret weapon for making delicate lines, sharpening edges, or removing stray bits of pastel. I always keep one inside my pastel box so it's at hand whenever I need it.
The cool thing about this tool is that it's capable of both dragging and lifting pastel pigment. I can make delicate, wispy blades of grass (this is especially nice when you want grass to overlap sky). Or I can use it to clean things up by removing pigment that's a little ragged or smudged.
Since it has the ability to both move and remove pigment, sometimes it might not do the thing you were hoping it would. The key to using this tool effectively is to use it in places where light and dark colors meet, and remember that it will always pull dark colors over lighter ones. So if you want to remove a dark smudge in a light area, it might be better to remove the dark pigment with a bristle brush or cover it with lighter pigments, rather than try to clean it up with this tool.