This ruling could lead to some confusion with the way other cards work.
Mariel Lewis is fairly straight forward - her send home says it removes the dude from the posse:
Shootout: If your posses has higher total influence than the opposing posse, remove a dude from the opposing posse and send them home without booting.
However some cards like
Pistol Whip:
Shootout: Boot your dude in this posse to send a dude in the other posse home booted. Your dude gets –1 bullets (minimum 0).
and Xiong “Wendy” Cheng:
Shootout, Boot: Send an opposing dude home booted.
don’t say they remove the dude from the posse after sending them home. I don’t have the rules/FAQ to hand so this might be covered there, but why does Eli leave the location of the shootout but remain in the posse while dudes that leave via Wendy and Pistol Whip don’t?