Hide logo on shared upload and download pages

Is there a way to hide the logo on said pages?

If a customer gets a link to upload a certain file, I don’t want them to click on the logo and see the login page.
If these pages get a certain css class in the body tag I can hide it using CSS, which is enough in this case.

I know it’s possible for the visitor to just go to the domain name of the page anyway, but I just don’t want people to have an easy option to go there.

Any idea about this?