Despite the fact that the wooden box fits very tightly into the suitcase, some of the outside edges still show. I covered the exposed wood with some of the same fabric I used to line the suitcase.
I used a bit of E-6000 glue to hold the fabric in place. I added glue along the front edge of the case and very carefully folded the fabric and glued it in place along that edge. After that was set I added more glue toward the back of the case to tack the fabric in another spot.
Basically, any unfinished wood that is visible when the wooden box is in the suitcase should be finished in some way - I added fabric.