The pipe is not actually an overflow, but is a vent in case of over pressure within the unit. The pipe is connected to a device I believe is called a "pressure relief device" which contains a small ball bearing which pops out if the shower head becomes blocked or the hose is kinked and allows the water to escape preventing the unit from exploding.
A spare part can be obtained from Triton spares, and is fairly easily replaced with a pozidrive screwdriver. To do this the cover needs removing, exposing the internal electrics, so PLEASE only attempt this if you are sure how to disconnect the power and make the unit safe!
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