Does recruiters ask for proofs when we say we have counter offer . Is it allowed to share offer letters?

The do, i simply smile. And nod as in " this is the deal, take it or leave it". Don't give too much respect to those rangoli idiots. Keep conservations minimum. They won't show us any respect when they fire us.

They do. Do not share your entire offer letter, but you can take the screenshot of the offer mail (not completely) and share that. If pressed, tell them that it is confidential and you'll never reveal confidential information.