Hi David, 

You can hide a particular component of a WebLink page by modifying its CSS. Specifically, you'll want to find the particular element that corresponds to the "My WebLink" button and hide it. Note, however, that this will hide this button across the board, for all users. For directions on how to do this with CSS, check out this Solution Exchange Article.

For more information on how you can customize the appearance and functionality of WebLink, take a look at the WebLink help files.