When someone repeats an argument that has been proven false /badly argued many times before, but keeps repeating it in hopes of drowning out opposition or derailing a thread. Yet not disruptive enough to get banned on forums, as it wraps itself in non-hostile, nicely written sentences.
How exactly do moderators deal with this kind of behaviour?
Neither of these really apply?
The big lie refers to a very big lie, but OP is talking about something subtle.
A gish gallop refers to many lies, such that an opponent cant refute all of them, but OP is talking about one lie.