DIAGNOSIS That's the anti-drip valve failing. It's a small rubber or silicone flap meant to seal the outlet when the pump stops. Mineral scale or coffee oils can cause it to stick open or deform.
FIX Run a thorough cleaning cycle. Fill the reservoir with a 50/50 mix of white vinegar and water, run a full brew cycle (without coffee), then run two cycles with plain water to rinse. The acidity can dissolve scale and free up the valve.
IF THAT DIDN'T WORK The valve itself might be warped or have a piece of debris permanently holding it open. Replacing it requires disassembling the showerhead assembly, which is tricky on this model.
HEADS UP Always put the empty carafe under the showerhead immediately after brewing to catch these inevitable drips. A persistently leaking valve will also drain the hot water tank back into the carafe over time, making your next brew start with lukewarm water.