Greyed out songs on my iPhone won't delete even after syncing on the computer?

I recently reinstalled windows on my computer and reinstalled iTunes as well. Last night I was having trouble with my phone and ended up system restoring it. Everything was backed up except my music (which I really don't care for anyway). Most of the things I downloaded ARE illegal and just automatically deleted upon plugging my iPhone in to my newly reloaded iTunes. Some songs however, those that are illegally downloaded by me are greyed on my iPhone but not showing up in my new iTunes, yet my actual legal purchases are coming on and off the iPhone while the greyed songs remain on the phone, prompting other people's Apple ID username and passwords (which is utterly annoying).Is there anyway to just delete the greyed songs? I know the answer can't be restoring the device because this is a result of restoring the device.

You answered your own quest. Unfortantly iphones build a software around installed files such as music and images, but if you really want to unlock potential i recognmend going to a mobile hospital it will cost a little but they have to teach you what you want to know… (there arent too many around) otherwise restoring would b hating yourself all over again, go to settings go to secure sorce area go to restore and don't enter the security code but proceed like you have then after it says please enter code go to itunes and playlists then edit playlist put the oldest songs at the top of the list then go to itunes and follow prompts to remove files done deal. I was scaring you at first but the truth is itunes.