Hi qouiou ,
Unfortunately, we currently don't have options to hide the button after an action or to move the widget on the page.
You could perhaps lower the
z-index of Buttonizer so that it would hide behind the popup.
Copy and paste this into WordPress' Additional CSS:
z-index: 999 !important;
These do sound like great features to have in the furture. I'll add this into our feature request list. 😄
If you have any questions, please let us know!