Check bounced to a guest for a hotel room and they are saying to keep it. i don't know what to do.

A guest was going to attend my wedding but ended up not being able to. She had already bought a hotel room and it was non-refundable. I was able to find someone to take the hotel room and they paid me for it, therefore I wrote a check to the guest who originally booked the room. Well the check I wrote bounced because I miscalculated funds.. weddings are crazy financially and there was a lot of movement in and out of my account. Anyways, she sent me a nice card explaining that she understands how living on a tight budget is and to keep the 200 as a gift. I don't feel comfortable with this because she lives in a tight budget and I want to send her the money. I don't want to offend her either. Any input on how to word giving her another check? She deserves the money, but I don't want to offend her either. Or do I just accept it?