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If you don't want to push these leads to SFDC, make sure that SFDC requires Full Name and/or Company and marketo will fail to sync. Those are the defaults, so it sounds like someone turned those off.
You can also control this to some degree by going to Admin>Integration>SFDC and making sure Sync Options default Last Name, etc are BLANK.
Also, if you have a central sync flow as Kate suggests, then your filters on the Smart List should exclude anyone missing key info or CONTAINS "[not provided]"