I would like to keep data in teradata that is non spatial attribute data and add spatial point data from a webapp storing data in a geodatabase (sql) and then sync the changes with the source data in teradata. What is the best method to use for database replication
You won't be able to use geodatabase replication since one is only a database and not a geodatabase. You would have to use some form a database replication, though I'm not sure if it's possible to create a replication between a SQL Server instance and Teradata. One recommendation would be not to version your feature classes that you are editing. This will create delta tables, which will store the edits until a compress occurs. Editing non-versioned feature classes will store everything in the base table.
As Jake said above- there will be no easy way to achieve this using ArcGIS tools as you will need at minimum two geodatabases for gdb replication. It looks like something similar to this might be possible, but will require some further research and extensibility: GoldenGate: Replicate data from SQLServer to TERADATA – Part 1 – GREPORA and GoldenGate: Replicate data from SQLServer to TERADATA – Part 2 – GREPORA