Jackie suggested I test whether a bit of heat and vinegar would make the silk color fast. I went off to the cupboard to see what kinds of vinegar we had which might work...we've got some Chinese varieties - Chinkiang vinegar, Chinese Black vinegar, rice wine vinegar, some expensive French white wine vinegar, some malt vinegar and several varieties of Balsamic vinegars...
I selected the rice wine vinegar as my 'best' choice of what I had in the pantry. I made a small skein of the pink silk. I dropped a couple table spoons of vinegar into a glass with some 'hot water on tap' - it's automatically at 190 degrees right out of the faucet. I dropped the silk in and waited until it cooled to room temperature. Then for the fun part - I got to check if any color would come out. As long as there was vinegar on the yarn it held fast. I washed it out in cold water with soap. No color. Then warmed up the water and lo and behold - the color started coming out.
It will be interesting to see if the over dye I did on this yarn will hold fast. That project is somewhat down the list of projects so it will be at least a month or so before I can say more.
PS I have, since then bought some distilled white vinegar for future dyeing tests and experimentation.