Just cut it off. Or, go into another department store which uses the tags (is it a hard white tag?) and ask that they remove it. Most stores/sales clerks will do it for you. If you don't want to go that route, just simply pry it and insert wire cutters SNAP! you are done. People rip/tear/cut those things off all the time without damaging the merchandise.

I highly doubt that you want to mail your jacket off to them, too many things can/will happen. Try and take care of it locally.