And don't ever clean the velvet strips with laundry soap, as the phosphate residue left behind will attach to the record. (Not a good thing)
Clean the velvet strips with the same record cleaning solution that you are currently using. Avoid using IPA (Iso-Propyl Alcohol) based solutions for cleaning the velvet strips, though, since the solvent may break down the glue used to hold the strips in place.
Avoid using tap water as a rinse, since most tap water is high in minerals. (Ever drain your hot water tank?) Imagine that on your record surface.