I have deleted a table, by exporting over the same table, and selecting the 'drop destination table before insertion'
As it turns out, we did have backups. I restored the backup on another server, and just copied the required table to the production database. Of course, I did it during such a time, where I was sure that no new records would have been saved. Just to be sure, I stopped the web application before doing this.

The idea came from the answer in the question that was linked by Darin Strait in the comments.