There might be some stricter requirements based on the food safety scheme you are under, however when it comes to rework, at a minimum you want to be sure the re-work meets your finished good standards and specifications and then verify that (color/moisture/pH/etc.). It also needs to be traceable, and the rework documented. It might also need to be placed in NCP if you have an NCP plan/procedure that calls that out (check your procedure, all the NCP programs I've run had re-work intertwined because it made sense for that).
To answer your specific question about frozen chili jam and re-cooking, you might have to wait until some experts in that area can chime in.