Hello,

the login module is mapped to a Responsivizer template position so obviously it shows up.
Unpublish the login module or the exclusions button to remove it from the mobile template.

Looking a bit deeper at the extension you will see that it works using modules matching between desktop/mobile template so you can build the mobile version of the website including only required elements.

An overview video tutorial to get basic concepts can be found here: https://youtu.be/B1fqydcZYlI

Best regards

John