Magento2 has this authentication pop up on checkout page, which many store owners wont like to see on their checkout page.
Background of this pop up area and Related files
The pop up itself is generated by Magento_Customer::account/authentication-popup.phtml
But this pop up works very differently on checkout page. In fact this is a separate pop up than the one you see in header area. It is embedded in a series of js files which are governed by knockout-js
Other file responsible is: vendor/magento/module-checkout/view/frontend/web/js/proceed-to-checkout.js
Here is how to remove it finally
Edit file or overload the file
app/design/frontend/YourVendor/YourTheme/Magento_Checkout/web/template/onepage.html
delete the following lines and save the file
<!-- ko foreach: getRegion('authentication') -->
<!-- ko template: getTemplate() --><!-- /ko -->
<!--/ko-->
Reference: