With increasing array size, it is increasingly important to control stray radiation inside the detector chips themselves. We demonstrate this effect with focal plane arrays of absorber coupled Lumped Element microwave Kinetic Inductance Detectors (LEKIDs) and lens-antenna coupled distributed quarter wavelength Microwave Kinetic Inductance Detectors (MKIDs). In these arrays the response from a point source at the pixel position is at a similar level to the stray response integrated over the entire chip area. For the antenna coupled arrays, we show that this effect can be suppressed by incorporating an on-chip stray light absorber. A similar method should be possible with the LEKID array, especially when they are lens coupled.