If you want to eliminate “Welcome Guest!” Would you like to log yourself in?” message completely, turn off the Customer Greeting in your Admin -> Configuration -> Layout settings -> Customer Greeting -> Show on Index Page and set to 0.
If you want to replace this message with one of your own, start your text editor and open the includes/languages/ENGLISH/index.php file and locate these lines of code:
if (STORE_STATUS == '0') {>>
define('TEXT_GREETING_GUEST', 'Welcome <span class="greetUser">Guest!</span> Would you like to <a href="%s">log yourself in</a>?');>>
} else {>>
define('TEXT_GREETING_GUEST', 'Welcome, please enjoy our online showcase.');>>
}>>
define('TEXT_GREETING_PERSONAL', 'Hello <span class="greetUser">%s</span>!');
As you can see, there are two Welcome messages depending upon whether you wish  Zen Cart to be a fully functioning store, or just a showroom.
Edit the message starting from the word “Welcome” but be careful not to change the text in angled brackets, or the brackets themselves. Make sure that the single quote marks are not left out. If you want to include an apostrophe in your text e.g. “Lucy's Store”, you will need to put an escape character before the apostrophe, i.e. “Lucy\'s Store”.
Save the edited file to includes/languages/ENGLISH/CUSTOM/index.php and upload it to your server.
Legend:
CAPITALIZED words refer to a folder or language that you choose. We use CUSTOM for your template and ENGLISH for your language by default. These generic terms should be changed to  the name of the  template/language you are using.