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Hi Damian, I completely that you shouldn't have to install a client to use TFS.
Unfortunately, only the most recently (v2015) libraries are licensed for redistribution, and these libraries require .NET 4.5, whereas BuildMaster v4 only requires .NET 4.0. These libraries also don't seem to connect to earlier versions of TFS unless VS2015 was actually installed; it's a bit frustrating for us, and other ISVs as you can imagine.
We have requested a redistribution license of the earlier libraries, and we can continue to explore getting it to work on our end, but it's not at all trivial.
The currently solution is to GAC the assemblies yourself or to install the TeamExplorer 2013 client, which does GAC these assemblies.