The Thread-Information Block should be widely known, and can be used to access a few important information. But can I use it to save data?
I've seen the structure has a slot for an arbitrary pointer at offset
You can use the TlsAlloc() function to allocate thread local storage. Each TLS index can save a pointer-sized value, so you can use a TLS slot to point to a larger allocated data structure if needed.
See Using Thread Local Storage for an example.