Dead moss etc
 

Both my front and back lawns have been treated with feed/weed and
mosskiller. I used a rake to get most of it up, but after further
treatment there are still a few small areas/patches of dead moss.
This also left the lawns looking bare and patchy!

I used a scarifier (rake on wheels) to get up all the old grass cuttings
and some of the dead moss, but there are still some areas left.

I intend to put a dressing layer on/in the depressed areas and re seed.

How important is it to get rid of ALL the dead moss, if at all?
Can any of it just be left and the seed over that area?

Thanks