Run a hairdryer on it to warm up the entire label/glue/luggage surface. Start with a corner and peel slowly, keeping the leading edge of the peel as warm as you're comfortable doing (I don't know what your bag is made out of).

That's worked for maybe 90% of adhered stickers/labels that I want to remove and if you do it right, no residue remains. Have even used it to get dealer decals off the back of a car.

I've never experienced the tag you describe so I have no idea what adhesive was used or if this method will work, but it's certainly worth a shot.