Concept of Hysteresis and Threshold point in Schmitt Trigger
In this case, the noise goes to -1V when the pulse is in a positive phase and to +1V when the pulse is in the negative phase.

Choosing +/- 1V as thresholds could cause the noise to change the output state when it should not because the noise is reaching the switching threshold. For the +/- 0.5V option, the noise would definitely cause unintended switching.

Therefore +/- 0.5V is not a good option.

As the total signal varies between +7V and -7V, the +/- 8V option would never change the output state.

The +/-2V option gives an extra 1V of noise immunity and (for the given task) would be suitable thresholds.

For the general case, the thresholds should also be below the noise free input signal; as we usually protect against noise up to a certain level, a noise free input should be part of the calculation.