Our game follows National Mah Jongg League rule. So whether you can undo a move or not depends what you're trying to undo and at what point.
Once you have discarded a tile, you cannot get it back and the game moves on.
If you call a tile but have not exposed yet, you can still change your mind about calling it, but once you've exposed, you're committed to an exposure, though you can change the number of tiles exposed. Once you discard, and end your turn, the exposure is locked in.
The way this rule manifests in our game is that when you press the Call button, you can choose pung/kong/quint or you can cancel (which is the same as if you had clicked Ignore).
Once you choose an exposure, you can change your mind on the number of tiles exposed (for example from kong to pung) by clicking the Change button above the exposure, but the Cancel button is not available since you've committed to an exposure.
Once you've discarded, you cannot change the exposure and are committed to it for the rest of the game.
If you claim Mah Jongg, you will get a confirmation message, so you can cancel out of it.
Keyword: undo, go back, changed my mind