The administrator controls the styles that are loaded in EndNote Web. If it is something others at your institution would want to do, then negotiate with the administrator to load a new style.
Otherwise, I suggest work in EndNote Web for your research & writing using any style, but swap to the desktop client for the final version. You can change the document from EndNote Web to the Desktop client (EndNote X5 > Preferences > Application). Then you can change the document to use your own edited style without brackets before submission.
Mary-Ann