Question on refunds using different CC card or check

[Collin Hays]

So Jane Doe makes a reservation in December for a June stay.  She pays a $200 deposit in December with her credit card ending in 1234.

Now she cancels, and tells us she no longer has that card, but she would like it refunded to a new card, ending in 5678.  Or, we write her a check and mail it to her.

What is the risk in doing this?  I assume the risk is that we write her a check or refund the "new" credit card, and then she charges back the $200 on the original credit card.  The guest defrauds us $200.

What are best practices on this?