There are numerous ways to finish small mats and this is just one way. Please use the method of your choice. Here is one way to finish small mats and it may be used for finishing your postcards. The photos I’m using are for some mug rugs that I’m in the process of finishing.
Draw a line around the outside of your finished mat (approximately 1 inch from last row of hooking). I use a ruler that I lay next to the last row of hooking.
Zigzag stitch around the mat just inside your drawn line and then stitch across corners.
Next, cut your backing off on the drawn line.
Pin foundation fabric to the back mitering corners in the following order:
a) Fold corners to back
b) Fold sides to the back
c) Pin (Back and Front)
Whip edge.
Stay tuned for the next post on how to attach fabric with labeling to the back of your mat.
Postcards From California 
Hi, I have my California Postcard finished. Should I mail it to you?
Arline
Arline, I’m very excited to see what you have come up with. I’ll be checking the mail each day until I receive it.
Gail