Operators cannot change thrust ratings, they can only change thrust limits.

You are confusing thrust ratings (which are design limits) with thrust limits, which are programmed in the FADEC. Two different things. a turbine engine may be rated for a certain thrust, but be limited to a lower MTO because of the aircraft in which it is installed. The former is fixed, the latter is programmed into the FADEC.

Turbine engines such as those used on the B737-800 have only two approved thrust ratings, the MTO (max takeoff thrust) and MCT (max continuous thrust). Everything else from there to idle are just manufacturer recommendations. The engines on the -800 are CFM56-7B engines rated at between 24,500 and 32,900 pounds thrust. If an operator wants their engines to last, and minimize repair maintenance costs, they will do things like not push the engines to MTO when it is not needed, and less thrust will do.

When anyone adjusts thrust in the FMS for a particular situation, for example, what they are doing is NOT changing thrust rating. What they are doing is changing thrust LIMITS, which the FMS them communicates to FADEC so it knows how to respond to pilot inputs in the throttle quadrant.