I figured out what's causing it. For some reason, the "Create contacts for auto-complete" setting in Gmail settings affects this. If you have "When I send a message to a new person, add them to Other Contacts so that I can auto-complete to them next time" selected, it will add any new email address used to your iPhone Gmail contacts. If you change the Gmail setting to "I'll add contacts myself," it doesn't happen.
The weird thing is that it does add it to the "Other contacts" in desktop Google Contacts, but not to the main "Contacts" group in desktop Google Contacts. Unfortunately, it seems that the iPhone Gmail contacts syncs both the "Contacts" group and any new email address added to the "Other contacts" group on desktop Google Contacts.
I don't want to have to use this work-around, because I like a previously used email address to auto-populate when I start typing in the To: field when composing an email in Gmail on desktop. I just don't want that email address added as a new contact in my iPhone Gmail contacts.
Maybe this is an iOS bug?
The instructions to change it if you want to do the work-around are from: https://support.google.com/accounts/answer/7345608