Depends probably on the nature of what “forwarded the costs” means.

If the business collected the costs from you and then forwarded them to CBP while acting as your agent, then you can demand a refund from them or sue them.

If you agreed to purchase goods for one price while also agreeing to pay a separate “tariff reimbursement fee” in exchange for purchasing the goods, you’re probably shit out of luck.

Various shades in between might be arguable or litigatable one way or another.