Hello,
I received an email to claim EOS airdrop, I would like to know if it is scam or legitimate

Indeed, many people claimed receiving those scam mails recently (hope no victims) after announcement of the date of EOS freeze in the old blockchain. Being a victim not only by proceeding links and offers their private keys to scammers; some scripts can easly be executed by your navigator and use your cpu to mine coins (see the cryptojack case). Should always be careful and never use emails received in spam folder or click any suspecious link.
Registering the wallet holding EOS doesn't need to use your ethereum private keys or passwords