It has nothing to do with Coach being printed on it. (In the case of fake bags, usually the more "Coach" markings an item has on it, the more likely it is to be fake.)
My opinion is that the scarf isn't counterfeit but rather, that it's a generic scarf to which someone added a Coach label.
The scarf doesn't have a print that Coach would use, the weave of the fabric isn't one that I've ever seen (not that that's definitive as to being fake), the brown label/tag appears to be added and has the wrong font and the scarf just isn't constructed as Coach scarves usually are.
Compare yours and mine:
Compare to various labels from different scarves, none of which are remotely similar to yours. Although Coach's middle name is "Inconsistency," it's the consistency that helps with authentications.