When I was trained in customer service, I was taught that the customer is always right. $20 or less that is lost will not replace the possible larger amount they may spend at your facility in the future. A lost customer, plus a bad word of mouth, will be a much greater loss to your company than handing over a few bucks for the sweaters.

Personally, I would apologize for the missing jackets, make it clear that you've searched the whole property for the jackets, but you are willing to compensate them if necessary. I would try to offer store credit/free day of boarding before offering cash (good way to see if they are actually being honest about losing their jackets, or just looking for some money.)