Why do pilots cut the reverse thrust below 40 km/h?
The question speaks of a very old 747 landing tutorial. And as such I take that to mean it would be of a 747-100/200 aircraft, and that's the reference point I'm answering from.

First, concerning the comments below the question that wonder whether you have to worry about unwanted objects on a runway at an international airport, there is no such thing as a completely clean runway, even after sweepers have just finished clearing the runway. There is always some grit—it's a matter of degree—and while ingesting it isn't going to cause immediate problems, over time it will abrade the fan blades and thus the engine performance. This may not apply to higher, body-mounted engines rather than engines mounted below the wing, at least we didn't worry about it when I was flying 727s. If our taxi speed with engines idle was getting a little fast, we would sometimes deploy the reversers of the center, S-duct engine in the tail for the taxi. 

Next, why take any risk if there's little benefit to be gained. The greatest effect of reverse power is immediately after touchdown when the aircraft speed is highest. As the speed slows, reverser effect decreases rapidly.


  (...) cut the reverse thrust after decelerating to 40 km/h.


40 km/h is only 22 knots. That's a taxi speed. I spent 10 years on 747-100/200 aircraft at two different carriers, and we never used powered reverse anywhere near taxi speed.

The 747-100/200 reverse levers are on the forward edge of the thrust levers. You can't raise them unless the thrust levers are in the idle position and the air-ground sensors show you on the ground. When you do raise them, they first come to a near vertical position that deploys the reversers but leaves engine power at idle. If you pull the reverse levers aft to get greater than idle reverse thrust, you're doing so against a spring loaded force such that if you relax the pressure, the engines will return to idle.


  What happens if that was ignored all the way to a complete stop? Would the plane start moving backwards?


Staying in reverse down to 0 km/h is simply not done. However, let's say you did it. If you had the reversers deployed but were at idle power, I doubt the aircraft would move backwards.  Reverse thrust is not as efficient as forward thrust. Depending on the engines and how heavy you are, 747-100/200s can start to move forward at idle forward thrust, but the usual procedure is to come to "breakaway" thrust to get the aircraft moving and then go back to idle.

If you came to 0 km/h in reverse with significant engine power, then, yes, you would start to move backward. But, of course, the chief pilot would hear about it, and probably fire you.

I know of one instance where a 747 was backed up using reverse thrust to clear a runway in an extreme situation in a third world country, so it can be done.