It sounds like a very nice item, I will just leave it as it is. If you decide to do embroidery on it I will just go with a simple and elegant monogram work. perhaps maybe some lace and then hand stitch it that way it wont be something that can risk the piece to be ruin.
Glad you have been able to remove the stains and not cause further problems. Like lindaavolio I would leave it as it is and make a tag to go with it
I wouldn't embroider on an antique table scarf I like the idea from lindaavolio.
I would do a Redwork design..but stitch it in an off white/tan thread, that way it will still look antique. I'm glad the dishwasher soap worked:)
I wouldn't embroider on it....you would lose ALL antique value. What I would do is embroider a gift tag with your name and date (also your friends name) and attach it with a ribbon and safty pin.
PLEASE DON'T RUIN THE VALUE...IT SOUNDS SO-O-O BEAUTIFUL!!!!!!!!!!!!!!! Good Luck