Tagline and Site title

Hello,
I just have a question: I set up a new header, but unde the settings appears “site title” and “tagline”. I think it´s very important to SEO, but the letters appear in my nice header, even when I mark “don´t display text”. I don´t want to delete this in the settings, but also don´t want to destroy my nice header. Is this tagline important or can it be deleted? Or how can this be done?