Hey Rob -
There really isn't any way to interrogate the .TDE directly to understand where the data came from - that is handled by the data source (TDS) which was in play when the extract was created.
Do you have access to the data source information (encapsulated as a TDS) which was used when generating the TDE?
I have access to the TDS, but is their a way to query the repository and get all the columns and tables used in the data connection?
Nope, no way to do that via the PostgreSQL database. Sorry. You're actually the first person I've seen interested in doing something like this - it makes for an interesting feature request. Maybe post this in the Ideas section?