It honestly will not harm the bow. It will get worse over time, but in my experience, will not ever come off. It just looks like crap. I think it is over catalyzed(it will become to brittle) or the film is too thick. Sometimes people stretch the limits of film thickness as it is done by a human.
After 43 years in the finishing business, I have even seen it happen on woodwork trim, doors, cabinets etc. It is almost always too thick of a film with catalyzed lacquers.
If I were in your situation, I would use it until the off season and send it back. I would put sleeves on it, or I use camo vet wrap on my bows for the season. It would irritate me enough to have to cover it.