Individuals living with paralysis or amputation can operate robotic prostheses using input signals based on their intent or attempt to move. Because sensory function is lost or diminished in these individuals, haptic feedback must be non-collocated. The intracortical brain computer interface (iBCI) has enabled a variety of neural prostheses for people with paralysis. An important attribute of the iBCI is that its input signal contains signal-independent noise. To understand the effects of signal-independent noise on a system with non-collocated haptic feedback and inform iBCI-based prostheses control strategies, we conducted an experiment with a conventional haptic interface as a proxy for the iBCI. Able-bodied users were tasked with locating an indentation within a virtual environment using input from their right hand. Non-collocated haptic feedback of the interaction forces in the virtual environment was augmented with noise of three different magnitudes and simultaneously rendered on users' left hands. We found increases in distance error of the guess of the indentation location, mean time per trial, mean peak absolute displacement and speed of tool movements during localization for the highest noise level compared to the other two levels. The findings suggest that users have a threshold of disturbance rejection and that they attempt to increase their signal-to-noise ratio through their exploratory actions.