In Batman V Superman movie, Diana received an email from Bruce Wayne:
How could a photo prove anything about her? The similar looking woman in the photo could be her grandmother. Or, it could be a photoshoped image.
Well, one assumes perhaps some of the following:
In particular, it was shown that there are entire files on potential metahumans.
These files clearly show the Flash employing his speed powers, Aquaman underwater without breathing for an extended period, and the transformation of Victor Stone by the Mother Box into Cyborg. While Diana's superpowers are not explicitly depicted (besides long life) it is implied that the files contain much more material.
In short, he is presenting the photo as quick evidence that he has reliable information to gain her attention by email, not necessarily presenting it as the only evidence he has that she is metahuman. The additional evidence is attached.
TL;DR It's basically clickbait.
The photo doesn't have to prove anything. The fact that somebody suspects is already bad news.
Diana has been living in secret for 100 years. She doesn't want anyone to know her true identity or history. So when somebody approaches her and says they know who she is, it doesn't matter whether they can prove it to the world or not. Just the fact that somebody suspects her is unsettling.
Think about it this way: if you were trying to hide something about your past, and somebody told you they knew what you were hiding, would it really matter whether they could prove it?