You are spot on: the group valve that you are referring to is the most likely culprit, It may well be that there is a bit of scale which is keeping it from closing completely.
You might want to remove and clean that valve before you do a full descale of the machine, see if that fixes that problem.
Be aware that if the machine hasn't been descaled in a long time, descaling may break chunks of scale off and those chunks might block that valve. You might need to do it a few times, and/or you might need to open the boiler and do a full manual descale just to get yourself in full control of a clean working machine.
Good luck.