According to your description, I recommend disabling this option via powershell commands which can be restored at any time.
This is the powershell command involved:
$claimMgr = Get-SPClaimProviderManager
$allUser = get-spclaimprovider –identity "AllUsers"
$allUser.IsEnabled = $false
$claimMgr.Update()
If you want to restore it, just let $allUser.IsEnabled=$true.
Reference:
https://social.technet.microsoft.com/Forums/sharepoint/en-US/ad63bd73-5070-493c-a358-30d4ab07cdcb/how-disable-everyone-group?forum=SP2016
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