Yes! It's homeless man from "The City on the Edge of Forever"
Clue #1
Starfish can quickly regrow appendages, unlike humans.
The "Homeless Man" steals McCoy's phaser. In the far away shot, you will see he is missing his ring finger on his right hand. Then, they show a close up of his hands holding the phaser, but now he has perfectly manecured hands and now he is not missing any fingers. Unfortunately, the regrown finger only survives a few more seconds before it is evaporated along with the rest of his body.
Clues #2 and #3
The soup is paid for by all with listening. And, Kirk shushes the man. Both clues come from the following dialog exchange.
MAN: You'll be sorry.
KIRK: Why?
MAN: You expect to eat for free or something? You got to listen to Goody Two-shoes.
EDITH: Now, as I'm sure somebody out there has said, it's time to pay for the soup.
MAN: Not that she's a bad-looking broad, but if she really wanted to help out a fella in need ...
KIRK: Shut up.
MAN: [tries to speak]
KIRK: Shut up!
Clue #4
The "homeless man" steals milk, then starts drinking it, and then drops the bottle and runs from the crazy McCoy. If asked if he stole the milk, he should plead his fifth amendment rights.
Bonus Clue
McCoy comments on the homeless man's "good cranial development" when he examines him.
Clue #5
He is curious about the phaser and ends up killing himself.