My favorite silk blouse had nametag glue on it. ~shudder~ The dry cleaner couldn’t get it out. I couldn’t wear it as it was, so I sprayed hair spray on the glue and washed it in gentle cycle, cold water. I even dried it in the dryer. “Dry clean only” silk. The glue came out. Yay!
I’m not suggesting you forego the dry cleaners but if they can’t get something out, and you have nothing to lose, might as well try this.
Lesson learned: Do not put a nametag on silk.