A Hum-X could help if both the modular and the amp have 3-wire AC connections. However, this sounds suspiciously like leakage across the busboard, TBH. First thing I'd do is to check the bus connection to the module on both ends and check for pin problems, debris in the ribbon connectors, that sort of thing. Then carefully reconnect the ribbon to the bus and module, feeling carefully to see if there's any resistance that doesn't feel quite right. If that doesn't work, then try replacing the ribbon cable itself, as there might be a broken wire in there that could be forcing leakage in some way.
Also, this is a good reason for investing in filtered busboards. Issues like this usually get sorted out by the filtering on the DC rails, which can be very useful if a certain module or two have a tendency to leak, as some older designs might. But yeah, this is a bit weirder and definitely more Eurorack-centric in terms of problems than a simple ground loop.