The answer to 'GFCI outlet burning smell' is that a burning smell from a GFCI (ground fault circuit interrupter) outlet is a serious issue that requires immediate attention. This could be caused by a short circuit, overloaded circuit, or a faulty GFCI device. The burning smell indicates an electrical problem that poses a fire hazard and should not be ignored.
If you detect a burning smell from a GFCI outlet, immediately turn off power to that circuit at the breaker box and do not use the outlet until the issue is resolved. This is not a DIY repair - you should call a licensed electrician to diagnose and fix the problem. Attempting to troubleshoot or repair a GFCI outlet with a burning smell yourself can be extremely dangerous and should be avoided.