The full text that displays by default: 

Welcome [First Name] [Last Name], (can't be changed)

Thank you for registering at our site.

Maintaining a close relationship with you is important to us. You will be receiving periodic e-mail updates from us.

You can help us serve you better by telling us more about yourself. The content of the web site as well as our e-mail updates can be personalized to your interests.

An e-mail will be sent to [email] with your user name and password. You can use this information to log into the site and personalize your web-site preferences.

Site Admins can edit this text by going to Setup > Site Options.  From here you can find the site options with the names: 
 

  • USER_QUICK_REG_THANKS_PARA_1
    • [[?[[S72:locale]]::en_US::<b>Thank you for registering at our site.</b>::[[M0:sdp_values:USER_QUICK_REG_THANKS_PARA_1]]]]
  • USER_QUICK_REG_THANKS_PARA_2
    • [[?[[S72:locale]]::en_US::Maintaining a close relationship with you is important to us.  You will be receiving periodic e-mail updates from us.  ::[[M0:sdp_values:USER_QUICK_REG_THANKS_PARA_2]]]]
  • USER_QUICK_REG_THANKS_PARA_3
    • [[?[[S72:locale]]::en_US::You can help us serve you better by telling us more about yourself. The content of the web site as well as our e-mail updates can be personalized to your interests.::[[M0:sdp_values:USER_QUICK_REG_THANKS_PARA_3]]]]
  • USER_QUICK_REG_SUCCESS_MESSAGE
    • [[?[[S72:locale]]::en_US::An e-mail will be sent to [[A3]] with your user name and password.  You can use this information to log into the site and personalize your web-site preferences.::[[M0:sdp_values:USER_QUICK_REG_SUCCESS_MESSAGE]]]]

You would choose which default wording would need to be changed and either clear all text and replace with your own or insert the text in between the double colons.

Example: 
[[?[[S72:locale]]::en_US::You can help us serve you better by telling us more about yourself. The content of the web site as well as our e-mail updates can be personalized to your interests.::[[M0:sdp_values:USER_QUICK_REG_THANKS_PARA_3]]]]

Change to

[[?[[S72:locale]]::en_US::Your New Text::[[M0:sdp_values:USER_QUICK_REG_THANKS_PARA_3]]]]

If you choose to remove all text then it would not automatically render default text for other languages.  (Note- Multi-Locale sites should not do this)