I don’t know any bank gift portal that permits redemption of reward points from debit / credit cards issued by different banks.
But I’m aware of a third party loyalty program called InterMiles.com (rebranding of Jet Airways’ JetPrivilegeMiles loyalty program), which permits reward points from different merchants to be converted into a single, uniform reward token called InterMiles, and redeemed on its website. If card-issuing banks have joined InterMiles as merchants, it should be possible to redeem reward points from multiple banks’ debit / credit cards on this single platform.