remove hover over alt/ title tag for home page

I am having trouble working out how to remove the yellow hover over title box for the home page from the main menu bar of my website. I removed all other title tags (for other pages and links) by removing the alt or title attribute from the code, and was wondering if anyone might know how to do the same for the home page, without using a plugin (as I feel that its a bit wasteful to install a plugin just for the sake of removing this one tag.) Thanks for any help.