Hi Peter,
Still trying to figure this one out.
The little Copy to Clipboard icon does not appear on 3 different test sites.
Tested on two Joomla 1.5.10 websites and one Joomla 1.5.8 website.
I was confused by another icon appearing.
After some research I have determined it is the Joomla 1.5 Legacy Mode icon.
Even on a website where Legacy Mode is Off, BetterPreview causes the icon to appear.
You can see this icon in your screenshot on JED here:
extensions.joomla.org//components/com_mt.../listings/m/6004.png
That Joomla icon to the left of the BetterPreview icon is the Legacy Mode icon.
On a website with Legacy Mode On, BetterPreview affects the icon position.
As soon as BetterPreview is enabled, the icon jumps further to the left of the "Legacy: 1.0" text about the width of another icon leaving a gap between the icon and the text.
I also discovered that if I publish another module to the status module position to the left of that icon, the Legacy mode icon disappears (even with BetterPreview enabled). This is on a website with Legacy Mode Off so the icon should not appear.
So the BetterPreview Plugin is somehow affecting the Legacy Mode icon.
Finally, on all three test websites I cannot see the BetterPreview Copy to Clipboard icon to the right (ever).
All three websites have many different extensions.
Did not test on a clean 1.5.10 installation.
Love BetterPreview.

This just has me confused.
Thanks.
KM
Edit: all three websites were tested with the current BetterPreview v1.3.0.