Lunchbox thinks Morgan is secretly engaged and had picture evidence to try and prove it.
He saw her wearing a ring on her engagement finger and took a picture of it to try and "prove" she was hiding that she's engaged. She was wearing a ring on that finger, but it was not an engagement ring. She said she was wearing it there because she is right-handed so it’s hard for her to wear rings on her right hand and that ring happens to fit well on that finger.
His advice for her was to not put a ring on that finger if she wanted to find a boyfriend because they may mistake it for her being taken.