A

Step 1: Understand the principle of buoyancy. When an object is floating, it displaces a volume of liquid equal to the weight of the object. In this case, the boat with the steel balls is displacing water equivalent to the weight of the boat plus the weight of the steel balls.
Step 2: When the steel balls are in the boat, they contribute to the total weight of the boat, leading to a certain amount of water being displaced.
Step 3: As steel balls are thrown into the tank one by one, the weight of the boat decreases, which means it displaces less water. However, the balls themselves will displace a volume of water equal to their own volume once they are submerged.
Step 4: The density of steel is greater than that of water, hence the volume of water displaced by the steel balls (when in the boat) is more than the volume of water they would displace when submerged. Once all balls are out, the boat is lighter and thus displaces less water.
Conclusion: The total effect is that the water level will remain unchanged overall because the decrease in the water displaced by the boat is offset by the water displaced by the steel balls submerged in the water.
Therefore, the correct answer is: A.