You'll notice that at the top of the pages it loads the xcgal_header.html template in the pages. That is where the button code is. Here is some code that should get rid of it. In the xcgal_header.html template, change (about 10 lines from the bottom):

<{if $admin_mode==1}>

to:

<{if $admin_mode==1 && $xoops_isadmin}>

That should take care of it for you (will remove display for registered users and leave it for module administrators).

I'll note that I totally redid almost all of the templates for this module (as I tend to do for almost every module). I also changed those buttons to simple links among other things (buttons weren't necessary).

You might also want to take the xcG/dev.xoops.org attribution out of the xcgal_footer.html, but that is up to you. Beyond learning to install and configure modules, learning to manipulate templates and learning Smarty is another powerful step for XOOPS admins. It's just HTML, generally.