If you want you can save them before you delete them. Just put a check on the box at the upper right corner of the page next to where is says messages and the count and then go to the bottom of the page where it says "Selected messages" and instead of Delete choose one of the other options such as "download as text" and hit go.That will save a copy of all your messages on your computer.Having done that you can then go back and do basically the same thing only this time choose "Delete" to clear your messages from HAMB's server.