I've seen some schematics where the LED is on a path used to power a circuit (or part of). It means if you remove the LED, the current won't flow, and the circuit won't work anymore. So, it depends on how it is implemented.

If you don't know the schematics, I would advise you to replace the LED by a short circuit instead of an open circuit.

Why? Because when the LED is ON, it has a small resistance (much lower than the current limiting resistor in series with it). And when the LED is OFF, the voltage across the LED is too low (under the its threshold voltage). So a short circuit wouldn't hurt in this case.

I don't know if a burnt LED is likely to be like an open circuit or a short circuit.

I've seen some schematics where the LED is on a path used to power a circuit (or part of). It means if you remove the LED, the current won't flow, and the circuit won't work anymore. Look at this one:

If you remove the LED, the circuit that is connected to CNTLED won't be powered by IC22C anymore. So, it depends on how it is implemented.

If you don't know the schematics, I would advise you to replace the LED by a short circuit instead of an open circuit.

Why? Because when the LED is ON, it has a small resistance (much lower than the current limiting resistor in series with it). And when the LED is OFF, the voltage across the LED is too low (under the its threshold voltage). So a short circuit wouldn't hurt in this case.

I don't know if a burnt LED is likely to be like an open circuit or a short circuit.