I have used this exact brand of pen for over 15 years. I have used it successfully on cotton, linen, all types of silk, and wool. I have never had a problem removing it, nor have i ever had the ink return after removal.
This is a water soluble fine line blue marker made specifically for fabric. When my work is completed, I spritz the work with cold water and let it air dry. Continue to check it over a couple of days to make sure you have removed all of the marks. If there are areas that are more heavily marked, it helps to dip a clean white fabric scrap in water and dab the area to remove any traces of the ink.