The phrase "delicate cycle" refers to a gentle setting on a washing machine that is used to wash delicate or fragile items, like lace or silk. It ensures a softer wash to protect the items from damage. Full definition
Hand wash using mild soap and water, or machine washed in cold water on delicate cycle using mild detergent. (chiccousa.com)
Next, machine - wash your clothes on delicate cycle by themselves or hand wash them. (blog.fitplanapp.com)
Then add your carrier to your machine with a mild detergent, set to your most delicate cycle, and choose a warm water temperature. (breastfeedbabywearclothdiaper.com)