iOS asks permission to access my gmail

Here's how:

1. Go to Settings > Mail, then tap Accounts.
2. Tap Add Account, then select your email provider.
3. Enter your email address and password.
4. If you see Next, tap Next and wait for Mail to verify your account.
5. If you see Save, tap Save.

Add an email account to your iPhone, iPad, or iPod touch

Create & use App Passwords

• Go to your Google Account.
• Select Security.
• Under "Signing in to Google," select App Passwords. You may need to sign in. ... 
• At the bottom, choose Select app and choose the app you using Select device and choose the device you're using. ... 
• Follow the instructions to enter the App Password. ... 
• Tap Done.

Sign in with App Passwords - Google Account Help

I am not clear about what permission you are referring to.

I have two of my Gmail account with the iOS mail app and it never asked for any additional permission except the email password and authentication because I have enabled 2 Step verification on Gmail