I got the question about what can be done to ensure that the plugin can be used after a clean install. I thought it might be helpful to others as well:
Depends on the version of T-Splines.
If 3.4 or earlier, then in %ProgramData%\TSplines\Rhino\ there will be a .lic file (it might be tsInstalled.lic or tsActivated.lic, or some other name, depending on how the plugin was installed). Be sure to keep a copy of that file. After the install, put the .lic back in the same original location. As long as you don’t change your ethernet card address, the license will continue to work.
If 3.5 or later, then follow these instructions: Support and Problem Solving | Autodesk Support
As an aside, I am no longer working at Autodesk, but last I heard the email address rhino.plug-ins.support@autodesk.com is still being monitored.