As stated in the Toad for Oracle 12.1 - Release Notes, this version introduced the following feature “When using Team Foundation Server (TFS) in Toad, you can now check-in TFS Work Items and link one or more TFS work items to the check-in change set.” In other words, it should be possible to associate work items with database changes while performing a check-in action from Toad for Oracle.
Additionally, the next version “Toad 12.5 supports Microsoft Team Foundation Server 2013 (TFS)”, as stated by Toad for Oracle 12.5 – Release Notes.
I am currently working with Toad 12.6.0.53 with Team Coding 7.1 – Trial, and I found out that the feature for associating work items during check-in unfortunately does not work out of the box on a client machine where Visual Studio 2013 Update 3 or Team Explorer for Visual Studio 2013 bits are installed. In order to solve the error you need to install Team Explorer for Visual Studio 2012.