Let me just start by saying this is a bug and I’ve documented it on idea station so you can all vote for the change.
If you have published a TP fitting to content center and you decide to change the authoring info there is no way to update the family in content center.
Sure, you can try the standard procedure of right-clicking on your family and use the Replace Family Template but that will not update authoring info.
Replace Family Template works (no errors) but the authoring info is not updated.
Creating a new CC family is not feasible because you then need to change all T&P styles for existing runs/routes and point them to the new family. T&P Styles uses the CC UID to track and store fittings of each style.
There is no other way except to cast a vote and to hope it gets implemented.
Here’s the link to idea station.