The Home link that you need to delete is not always in the header.php file. For example, if the header file calls a function like “nav” or “menu” then the Home link may be in the Theme Functions file.
I just fixed the duplicate Home page problem by editing the functions.php file in one theme.
Might be in other places too, but you should find a reference to it in your header.php file. It is then a matter of tracking it down and experimenting to see what works in your theme. I use the WordPress Theme Editor for this. Remember to make a copy of any code that you delete so you can put it back!