Itunes syncs unchecked songs?

Itunes syncs unchecked songs?

Added (1). The only thing is that they don't play and they have a cloud next to them. I just want them off my iPhone but left on my computer.

Added (2). also yes, I have checked off "Sync only checked music"

Why don't use iTools instead of itunes? Search in google about "itools english version", open the blog, and download it.

iTools is much more easier to import/export/delete songs.