My 1st generation Motion Detector was tripped and now there doesn't seem to be a way to reset the sensor back to its "cleared" mode so it can detect further movement?
No. Motion Detectors have a built-in function called "dwell time." Dwell time means that after a Motion Detector is tripped it will need a three-minute period in which it detects no motion in order to "reset" back to its default detection mode. This prevents the sensor from sending out multiple alerts for the same motion.
To reset the Detector, clear the detection area of anything that might create motion (such as you, your kids, or your pets) for a full three minutes.