Dry cleaning is read as careful, professional cleansing of something delicate. Tradition takes it as handing a sensitive matter to someone else to sort out.
When this appeared in your dream, what were you feeling?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.