I think this is “Something Green” by Fredric Brown.
Red planet. Check.
The big sun was crimson in a violet sky. At the edge of the brown plain, doted with brown bushes, lay the red jungle.
Sentient hand. Check.
The little five-limbed creature that rested on his shoulder didn’t answer, but then it never did. It couldn’t talk, but it was something to talk to. It was company. In size and weight it felt amazingly like a hand resting on his shoulder.
No green. Check.
"The most beautiful color in the universe, Dorothy. Green! And I know where there’s a world that’s mostly green, and we’re going to get there, you and I. Sure we are. It’s the world I came from, and it’s the most beautiful place there is, Dorothy. You’ll love it."
However, this dates from 1951, so this might not be the story you read, if you're sure it was more recent. Perhaps a reboot.