Hey Annoying_pop_up,
We’d be happy to help out with getting your Google account password updated. If for some reason you’re unable to just update the information when noticing the pop up, we’d suggest just removing the account and adding it back with the correct password. You can do so safely without any data loss since Google accounts are preconfigured IMAP accounts and all the information associated with them are stored on their servers, not locally.
For help, check out these steps:
Log out of or remove email accounts
1. Go to Settings
> Mail > Accounts.
2. Tap the email account you want to remove, then do one of the following:
* If you’re removing an iCloud email account: Tap iCloud, tap iCloud Mail, then turn off "Use on this iPad”.
* If you’re removing another email account: Turn off Mail.
* Note: To remove the email account from all apps on your iPad, tap Delete Account.
This is outlined further here: Add and remove email accounts on iPad - Apple Support
Once completed, add your account back with these steps: Add an email account to your iPhone, iPad, or iPod touch - Apple Support
We hope this helps out.
Take care!