Moving the hub from one socket to another indicates the presence of unfiltered extension wiring, which in itself tends to be a problem for FTTC. It won't necessarily be solved by plugging the hub into a different socket because the extension wiring will still be connected to the line. Filtering off all the extension wiring with a filtered faceplate is a possibility, if they have a modern NTE5 type master socket, and if the extension wiring is connected to the master socket. But they might not have a modern master socket, and even if they do, there might still be extension wiring connected to the line at some junction box elsewhere.
How could removing the faceplate break their connection? Well, you could remove the faceplate, and old brittle poorly secured bits of wire could detach from the faceplate or even break. Yes, sure, you could probably reconnect everything quite easily, assuming the remaining bits of wire are long enough. There's always an element of risk that something will go wrong or you'll make something worse somehow.