Strippers typically remove stains that have pigment in them. The reason for this is that the pigment needs to be mixed with a diluted finish so that it stays in place. Pigmented stains sit "on th and e wood"are used to give an even "paint" like color to the wood, and is translucent. Dye stains go into the wood, and are translucent.
My guess is that you have a dye stained piece. The best way to remove ( or lighten) these stains is bleach.
What I'd try first is an application or 2 of laundry bleach. Apply directly to surface, let sit overnight, and, if needed, apply a 2nd coat and let dry. Once dry wipe down surface with a diluted white vinegar solution, let dry, light sand with a 220 grit, remove dust and stain and/or finish. If laundry bleach doesn't work, then use the 2 part bleach, following directions on can.
Bob "Boardman" Borders