That grease is just exastberating your itches (although you don't know it). If you have a dry scalp, jojoba oil (as the carrier oil) mixed with a few drops of essential oils like rosemary, lavendar and/or peppermint (a favorite 'cause it's minty and wakes up your scalp) are great.
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Grease on the scalp also can prevent growth and prevent natural oils from getting to your hair.