Hi Tee Emm,
de facto and lomapaseo gave you some good information regarding your questions and I am going to attempt to give you a good technical explanation.
Generally, there are 4 key thrust settings that are addressed by the power management control (PMC) system in the CFM56-3 engine:
1. TO - takeoff thrust
2. GA- go around thrust
3. MCL - maximum climb thrust
4. MCT - maximum continuous thrust
The takeoff rated thrust is the highest thrust rating given by CFMI for operational use by the aircraft manufacturer, in this case, Boeing. The thrust rating is based on maximum allowable EGT level at which the engine is allowed to operate at for 5 minutes. For a constant EGT value, engine thrust varies inversely with ambient temperature. The maximum EGT level is specified at sea level altitude and a specific ambient temperature that is higher than standard atmosphere conditions, usually between +27 to 36℉. This takes into account hot day aircraft performance requirements with no operating penalty. Now there are some exceptions to this.
Some airlines have negotiated increased takeoff and maximum continuous thrust levels to tailor an aircraft performance for high airport elevations or high ambient temperatures or both. This allows the airline customer to operate the engine at increased thrust and EGT levels and is often referred to as a bump rating. The earlier generation PMC's, as used for the CFM56-3, are analog electronic controls with input signals of N1, Power lever angle (PLA), fan inlet temperature (N2) and fan inlet static pressure. Since the fan and core engine is linked, the core speed is monitored and limited to prevent overspeed. There is a limited override of the core speed schedule in a limited PLA range, usually in the takeoff or maximum climb PLA regions. Fan speed is controlled as a function of T2 which is known as corrected fan speed. Effectively, the EGT is not limited, but only reported if it is exceeded.
When a new engine is final assembled, it is tested, among other things, to determine the EGT margin at takeoff conditions. The engine is guaranteed to have a certain % EGT margin to maximum allowed EGT and this testing confirms this. Then when the engine goes into service over time and cycles, the EGT margin decreases. This decrease is most often due to airfoil tip seals wearing in the compressor, HP and LP turbines, but other factors such as combustor flame pattern changes, HP air-cooled turbine airfoils becoming less effectively cooled, etc. So this degrading EGT margin becomes most apparent during high power settings, MCL, MCT, GA and particularly on those engines that have "bump" ratings. What is generally experienced is what I call an EGT overshoot.
When this happens, the engine does require an examination, generally a boroscope inspection of the compressor and HP & LP turbines to make sure the components are within operating conditions. Obviously, this makes airline management unhappy because of scheduling and aircraft utilization downtime that is experienced. However, in most cases, no damage is done by the EGT overshoot except for the fact it adds to the deteriorating EGT margin where at a point in time the engine must be removed and fully serviced. Certainly one would not want to limit thrust in a critical situation because of a momentary EGT excursion. OTOH, it would be desirable not to use high thrust settings for situations when it is not needed or just because it is available.
I hope this helps answer your question regarding EGT overshoots.
TD