Remove the shavings if you can, it'll not only tap nitrogen, it'll settle as they decay off. That leads to nasty dips in your lawn.

Inevitably, you won't be able to get all the bits of wood out. That's OK, during cooler weather you can fertilize just a little extra (maybe ten to twenty percent) in those locales to keep nitrogen levels up. I generally recommend the use of Milorganite or soybean meal as the nitrogen release is slower, gives the grass a good chance at getting enough, and also supplies plenty for the wood to rot.

Since you may still get settling, you can add up to a quarter inch of top soil at a time to those areas to start re-adjusting them. The grass will grow right over it. Repeat once every six weeks until the soil levels out.

I concur. I had 10 trees removed a year ago and sawdust was left in the holes. Those spots have already settled about 2" and the grass visibly suffered. Just a week ago I filled those spots with good top soil and reseeded. You're going to have to do the work sooner or later, so you might as well get it done now.

Okay, thank you!

Morpheuspa, that's interesting about adding a little topsoil at a time to level out ruts. (Maybe not a good thing for OCD people like me to know about....)

It works, and I'm probably no less OCD on my lawn than you are. :)

At this point there is not one single spot that sticks up or dips down anywhere.

Um... you win. :)