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If I've understood you properly, you have software which backs up user specified databases and their tables, in which case I don't have any idea how you could get the information if you've never seen...

Multi-posted here:
http://www.javaprogrammingforums.com/jdbc-databases/13287-how-get-last-modification-time-ms-access-database-table-using-java.html

You have a few options here, you could either;
1.) Use database triggers
2.) Have a "Last updated" column in your table, and update it with a Date object whenever an update/insertion is performed
...