Steps to reproduce:

1. Start with a template and some (valid) TemplateData for it.
2. Change the template, so that parameter_X is now called thingabob_Y.
3. Decide that you need to update the TemplateData. Decide that, while you're at it, you'll improve the TemplateData.
   1. Rearrange the order of the parameters.
   2. Save the page.
   3. Change parameter_X to thingabob_Y.
   4. Save the page.
   5. Get (accurate) error message that there is an Invalid value for property "paramOrder[13]".

Results:

If you look at the ParamOrder section of the JSON, the parameter order list still shows the old name. If you manually fix the name, it saves with no difficulty.