That is actually a humorous question to me, because "everyone and their brother" had been wanting SharePoint to have breadcrumb functionality built-in. Now that it does, you want to get rid of it 
Now, as for removing the breadcrumbs....you will probably have to edit the master pages for this to work. All the SharePoint pages are not really full web pages at all. They are built on the fly using different settings from different files.
You will need to use Microsoft SharePoint Designer to edit the files. Honestly, I would stay away from doing so if at all possible (especially if you don't know what you are doing). This is very dangerous and can totally miss-up your environment. Also, if you remove breadcrumbs from the master page, you will be removing it from all pages (including other sites).
If it were me, I might just live with the breadcrumbs being there. I know it is what the security professionals would call "information leakage", but in this kind of area, I personally wouldn't fret it.
-dggcoop, MCTS
Cick here for my blogPlease do not email me your SharePoint questions! If you need SharePoint help, please post your question in the appropriate SharePointU.com forum.
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