Blondie12 gave some great advice- Try Dawn Dish Soap- it will break down any oils which you might be feeling on your system. You will want to use the standard blue one, nothing with any moisturizers.
I'm not sure why your system would feel greasy as a new unit- but sometimes solvents can leave a residue, or even some styling products.
If you continue to have issues, please feel free to e-mail me photos, or you are also welcome to send the unit back for us to look at and fix whatever may be causing this.
Emily | Hair Replacement Consultant | firstname.lastname@example.org