[M_a_t_t]

Just what I've read:
When shops change the fluid they typically use a pressurized pump that goes in the opposite direction of flow when the engine is running. This knocks debris loose and causes this issue.

Whether this is true I don't know, but if you want to change it I would recommend disconnecting a cooler line and let it pump a quart or two out. Turn the car off. Add the same amount. Rinse and repeat until the fluid coming out of the cooler line is clean.

I don't know if this applies to all A/T's, because of the cooler location in the flow path.