DIAGNOSIS The gears in the pan/tilt mechanism are likely obstructed. Dust, a stray hair, or even a tiny bug can get into the gears and cause that awful grinding sound.
FIX Power the camera off. Gently tilt the camera ball all the way up and look into the base's socket. Use a can of compressed air (like for keyboards) to give several short bursts into the gear tracks around the edge. Rotate the camera by hand gently to expose new areas and repeat. Power it back on and test the movement in the app.
IF THAT DIDN'T WORK The obstruction might be more stubborn. With the power off, you can very carefully use a cotton swab slightly dampened with isopropyl alcohol to wipe the visible gear teeth, being sure not to leave any fibers behind. Let it dry completely before powering on.
HEADS UP Never force the camera to move by hand while it's powered on. You can strip the plastic gears. Always use the app to control it, or power it off first if you're inspecting it.