I've used the following workaround on other PC's for 10.2.2 and maybe 10.3.1, so I'm not sure it will work for 10.4
1. Uninstall ArcGIS Desktop 10.4
2. Install ArcGIS Desktop 10.1 (or whatever version matches the GDBT tool version)
3. Install GDBT (since the ArcGIS desktop version the install wanted is now present, the install can continue)
4. Uninstall ArcGIS 10.1
5. Install ArcGIS Desktop 10.4
6. Open ArcCatalog and the GDBT tab should be there and work....at least for the version state tree which is all I ever use from the tool these days.
I don't think anything has every changed in the ArcGIS Desktop software that would actually break the tool, the install just does this check to see if the version matches, and if it doesn't it won't install.
-Andrew