"Photo Finish," or too much time on my hands

[snopes]

Barbara recently wrote a page about the "Photo Finish" legend, to which I added a description and clip of its well known use in an episode of M*A*S*H.

Today I was thinking about the legend's presentation in the M*A*S*H version. It starts with a wounded soldier reading a "Dear John" letter he has received from Gloria, his girlfriend back in the United States:

I'm engaged to Rob Webster. I doubt you know him, but perhaps you've heard of his family. They own the bank. I'm sure you can understand why it would be best if prominent people like that didn't know about my relationship with you. If you really do care about me, you won't mind sending back my picture.

Now, how is this soldier's having a picture of Gloria going to clue in the "prominent people" back home that he and Gloria once had a relationship? He's probably not going to encounter anybody in Korea who knows Gloria's fiancé's family, and even if he sent the photo to someone back home it wouldn't prove anything, because it's just a picture of Gloria and not the two of them together. (Otherwise, Hawkeye's scheme of also mailing Gloria photos of a bunch of different women wouldn't be feasible.) Maybe the soldier could cause a fuss by showing the photo around himself once he returned home, but by then Gloria would probably already be married.

And all of this overlooks the plain fact that by writing a letter asking for the return of her photo, Gloria is providing the soldier with essentially indisputable proof that they once had a relationship ...

- snopes

[Base Ten]

I'm pretty sure there was no mention of this in the episode, but perhaps there was something written on the back of the picture.
Something NFBSK?

Base Ten