Not sure if you read all the posts here. The owner said he does not want the pigeon.I'd suggest to let it continue on its way but that doesn't mean you can't feed it and give it water and let it have some strength first.
https://www.backyardchickens.com/threads/can-i-keep-a-lost-pigeon.1420964/post-23373589
So are you suggesting the OP lets loose this pigeon so it can get lost a second time,

