Make part of fill transparent

Working with an eps file that was sent to me, I am attempting to make the pink inside of the area transparent while leaving the outer part (lower part of the image) - which appears to be a stroke, but it's not. I have attempted to add a stroke and remove the fill, it does not line up correctly; I've done this with both the white and pink areas.  Using a paint.net and the magic wand I can achieve this as in the image below but I cannot remember how to in Illustrator (maybe it's too early in the day).