We introduce the problem of Table Reclamation. Given a Source Table and a large table repository, reclamation finds a set of tables that, when integrated, reproduce the source table as closely as possible. Unlike query discovery problems like Query-by-Example or by-Target, Table Reclamation focuses on reclaiming the data in the Source Table as fully as possible using real tables that may be incomplete or inconsistent. To do this, we define a new measure of table similarity, called error-aware instance similarity, to measure how close a reclaimed table is to a Source Table, a measure grounded in instance similarity used in data exchange. Our search covers not only SELECT-PROJECT- JOIN queries, but integration queries with unions, outerjoins, and the unary operators subsumption and complementation that have been shown to be important in data integration and fusion. Using reclamation, a data scientist can understand if any tables in a repository can be used to exactly reclaim a tuple in the Source. If not, one can understand if this is due to differences in values or to incompleteness in the data. Our solution, Gen-T, performs table discovery to retrieve a set of candidate tables from the table repository, filters these down to a set of originating tables, then integrates these tables to reclaim the Source as closely as possible. We show that our solution, while approximate, is accurate, efficient and scalable in the size of the table repository with experiments on real data lakes containing up to 15K tables, where the average number of tuples varies from small (web tables) to extremely large (open data tables) up to 1M tuples.