It's not your fault. When the site's design was updated on 2010 March 18, the delete button (a small 'x' in the upper right hand corner of each of your synth cards) was accidentally masked.
This has been discovered and reported and the Photosynth team is working on a fix.
For the time being, though, as long as you are signed into your account on the site and have clicked on the 'My Photosynths' link at the top of the site (in your case, you should be looking at one of the following links:
you should still be able to use the button even though you cannot see it.
Imagine a 1 centimetre square box in the top right hand corner of any synth card and hover your mouse cursor in the middle of this space. You should observe the cursor changing and clicking in this space will pull up the warning asking you to confirm you really wish to delete.