When you change your Gmail password on the Gmail website, you need to update your Gmail password on your iPhone. Otherwise, you will not be able to sync your Gmail account with your iPhone's Mail app. Update your Gmail account information in your iPhone's mail settings.
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Open your iPhone's Settings app and then tap Mail, Contacts, Calendars.
Tap the Gmail account you want to update.
Tap Account to access your Gmail account settings.
Tap Password, and then enter your new password.
Tap Done to submit your new Gmail account information and authenticate your account.