There is a way to fix this issue. Bookmark this URL: https://mail.google.com/mail/?labs=0 and use it to open Gmail. This URL is used to load Gmail without enabling labs. Surprisingly, if you manually disable all the Gmail labs experiments, the close button is still there.
If you use Greasemonkey, you can create a new user script using the code from this page.
Another way to fix this issue is to install AdBlock/Adblock Plus and manually add this rule in the preferences:
Google is working on a fix. Apparently, this is a leftover from the "about the new look" message that used to be displayed when Gmail launched a new interface back in 2011.
Update (March 21st): Fixed.