When you are signed into your account and you click on the 'x' in the top right corner of the card for a synth or pano, you should get a message box that reads:
"Are you sure that you want to delete this synth? [ OK ] [ Cancel ]"
Naturally, if you click 'OK', then the synth will be permanently deleted from the servers.
What version of which web browser are you using and could you please try a different web browser?
Here are links to the most common ones: