You can only delete an experiment if you are the uploader or the PR of the experiment. Marking an experiment as deleted actually does not delete the experiment immediately, but instead moves it to the trash. Experiments can be removed from the trash after accessing the trash from the navigation bar.
Log in to Cytobank and click on the Inbox link. Select the experiments you want to delete by clicking on the checkbox next to them and click on the button named "Delete". This will move your experiments to the "Trash".
Alternately, you can delete an experiment by clicking "Delete" under the "Actions" dropdown menu on the experiment level navigation bar (within an experiment).