This is a modified version of the GibbedTools package created by the Magic The Gathering modding community, I added support for Carmageddon: Reincarnation textures and normal maps.
Download it here: http://trent.incarnated.co.uk/downloads/GibbedTools.zip
Extract the RAR file to a folder somewhere, it doesn't matter where.
Decompiling TDX files
Drag the TDX file onto Gibbed.Duels.TdxConvert.exe and it will automagically make a PNG image of the same name. When you open the PNG it will probably be mostly transparent, this is because the transparency controls how reflective the surface is. In Photoshop you can use Layer->Layer Mask->From Transparency to create an alpha channel from the image's opacity, you can then fill the alpha channel with white to make it opaque. However, it is a good idea to copy the contents of the alpha channel into a new layer so you can put it back into the alpha channel after you've finished editing the texture.
Compiling Textures to TDX files
Most textures can be compiled by dragging the PNG file over CompressDXT5.bat, which will create a TDX file of the same name using DXT5 compression.
However if you're compiling a Normal Map you must use CompressNormals.bat instead as Normal Maps require their own compression algorithm.
The source code for the GibbedTools is provided, you can open the Gibbed.Duels.TdxConvert.sln in Visual Studio (you can use VS Express) and edit it to your heart's content. It is written in C# so it's fairly easy to understand. You can probably tell which bits of code are mine by how bad they are (e.g. everything in BC5Unorm.cs)