Hi;
I have a guess but I'm not sure I'm gonna be able to explain it correctly (maybe I'll not find the correct words).
There is a plastic sheet under the keyborad and this sheet has molded bubbles under each key. In the inner of each bubble, right in the middle, there's a conductive "circle" (like a black, carbon spot) and when a key is pressed, this conductive spot touches two conductive paths, array-type arrangement, right below it. The conductive paths are printed in a separated plastic sheet, connected to the calculator's circuitry.
I guess that the bubble under the [4] key in your calculator has some sort of irregularity or it has fissures. Each key has a small pin that slight glides over the respective bubble's surface when the key is pressed, and it glides back over the same path when the key is released. If the supposed irregularity is right over this gliding path, when the key is released the pin is forced over it and loudly clicks.
If you want to try a brief test, please slowly press the key and try to sense any irregularity or hear a soft sound. If it happens, stop pressing it and them release it slowly. You'll probably hear the loud click if it happens this way.
I cannot figure a solution out of this other than opening the keyboard, what needs opening the calculator first.
Hope this helps identifying the aggressor.
Best regards.
(Please, if someone understood, agrees with it and wants to improve the explanation with better terminology, be my guest)