  We evaluate the quantum witness based on the no-signaling-in-time condition
of a damped two-level system for nonselective generalized measurements of
varying strength. We explicitly compute its dependence on the measurement
strength for a generic example. We find a vanishing derivative for weak
measurements and an infinite derivative in the limit of projective
measurements. The quantum witness is hence mostly insensitive to the strength
of the measurement in the weak measurement regime and displays a singular,
extremely sensitive dependence for strong measurements. We finally relate this
behavior to that of the measurement disturbance defined in terms of the
fidelity between pre-measurement and post-measurement states.
