If you want to remove a Gmail account from your iPhone without deleting it, follow these steps.
1) Go to the Settings app on your iPhone and tap Mail, Contacts, Calendars under Mail 2) Tap Add Account 3) Scroll down and select Exchange Server 4) Enter the name of the email address that is associated with this account 5) Type in an alternate email address for contacts or calendar if desired 6) Tap Next 7). The next screen will ask you which type of mailboxes (Outlook/Exchange/Gmail), click on Outlook 8). At this point, switch back to Googles webpage
9): On Googles webpage enter your username password 9a). After logging into Gmail go back 10); In order for iCloud calendars to sync properly make sure You have selected Email as Calendar option. This should be done at step 8