Is the offer of a refund in writing (well, email)?
Is the offer of a refund from Fitbit themselves or from the retailer?
If it's from the retailer, is it from someone with a substantial presence and reputation (John Lewis, Dixons, Amazon, that sort of thing), or is it from Fred's Fitness Fings, an ebay outlet with a feedback score of 3?
(Yes, I know those are a bit rhetorical because you've given the detail in your post, but given you've got a written offer of a refund from Fitbit, do you really think it's likely that they're going to renege on it? If you are unhappy enough with it to want your money back, then I'd be surprised if you had any difficulty taking their offer at face value.)