I'm going with, that she wanted the actual photo back. She doesn't care if anyone knows about her. She was just looking for her photo of her love. How do you think Lex got the jpeg, he made a copy from the actual photo.

The "He has a photo of me" thing was just her cover story. Diana was investigating to see if Luthor knew anything damaging about her and the Amazons.
It's just coincidence that there WAS an old Photo of her in the records.

Sentimental value.
Which would be worse - to live as a monster, or to die as a good man?

It's almost like this movie is poorly written or something.
If you can't defend a movie without bashing another, you will be put on ignore. No exceptions.

Lol! She has applied that reading glasses technique before
Yeah, it's the most ridiculous angle I have ever seen.
Lex could put the picture on facebook at that point.
What got me, was she couldn't crack the hard drive open, and decides to leave on a commercial air flight.
I'm like what is THIS?! She tucks tail and goes back home?
Just ridiculous.

It is extremely confusing as to why she is trying to get a digital file back, is she unaware that Lex may have as many back up files as he wants or that he may even have the file stored on the cloud? The could easily have denied the person in the photo was her or that the photo was fake or if worst comes to worst put on a pair of glasses and then no one in the DCEU would ever recognise her anyway.
To make a great film you need three things - the script, the script and the script -Alfred Hitchcock

Everyone is confused. Why would a god care about a picture that was already turned into a jpeg file?

Right. She visited Man's World after hunky Chris Pine washes up on shore followed by a bunch of Germans, gets involved in wild wacky WW1 stuff and then.something happens that causes her to turn her back on the world and go back to Paradise Island (my guess? Either hunky Chris Pine dies or hunky Chris Pine is involved via the military in some pretty unheroic acts during the war that shatters her "good guys/bad guys" outlook on things. you can also add in "everything goes well but the military/President want to suppress her because she's "just a woman" if they go with a grrrrl power movie) and then something motivates her to come back after a century long absence. Hopefully the movie addresses this.but I can only hope given the past outings.

Thanks for the reply.
Hopefully WW's film will explain the photo in detail as from the trailers, it sounds like she's in the present explaining what happened to her in the past.

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Okay, best I can give you here:
Her own investigations prior to her appearance in the movie led her to know Lex had obtained this photo.
The photo was important (probably) because it showed there was an immortal person running around fighting the war 100 years ago. Of course, why that would matter since she had bowed out of mans world for 100 years makes little sense. But presumably, she has a reason for coming back and does not want her age revealed.
Lex was interested because he was compiling data on all metahumans and Wonder woman certainly applies.
As for the last part (and this is all conjecture that I'll foolishly hold out hope is discussed in the Wonder Woman movie), WWI was before there were newsreels, embedded reporters, video cameras, etc. So if Wonder Woman was not running around in Manhattan or London or Paris but was on the actual battlefields, she was not known to the general public. Add to that it was a time when women as a rule were very much treated like second class citizens and there is NO way the military would widely advertise that a super-powered woman was mopping up the floor with the Germans.