You can delete them through the database. If you have phpMyAdmin available to you for accessing your database, go into the postmeta table (usually wp_postmeta), browse the records, and delete those you no longer want around.
A fast way to hit multiple records at once is to use a SQL query statement like this:
DELETE FROM wp_postmeta WHERE meta_key = 'syndication_source';
Just change the table prefix (wp_) if not using the default. Run a DELETE query on each meta_key value you want to remove.
Warning: Backing up (exporting) your database before doing anything like this is a Good Thing™.