There may be situations where this form of argument is legitimate, although I might phrase it a bit differently:
A: I'm an eliminativist. I don't believe that love exists. The commonly-understood notion of love is nonsensical because [...].
B: What do you think is actually happening to a person who thinks she's in love?
A: I don't know. Eventually, neuroscience will figure that out.
B: OK. Until that happens, do you mind if the rest of us continue to use the word "love" to describe this scenario?
A: Yes, I do mind. Nobody has proven that love exists. The burden of proof is on you, not me.
B: Since you have provided no alternative label for this scenario, we need to call it something, and "love" is convenient and commonly understood, I'm going to keep using that word anyway.
(This is a deliberately simplistic caricature of eliminativism, used to make a point. It should not be mistaken for a real argument against eliminativism.)
From a scientific point of view, a theory can be falsified in one domain, but still produce good results in another. For example, it was long known that Newtonian gravity fails to accurately describe the precession of Mercury (although at the time they believed there must have been an additional planet to account for this, rather than the theory actually being wrong). Nevertheless, people continued to use Newton, and they still do today, even though general relativity is strictly more accurate. Newton, as it happens, is easier to calculate, and produces results that are just as good under a variety of real-world situations. This is because Newtonian gravity is an empirically-validated theory. That is, Newton didn't just make numbers and formulas up and write them down. He tested and refined his theory against the real world. Any theory of gravity that wants to replace Newton had better produce the same results as Newton observed under those conditions, or else it's empirically wrong. But if no viable theory can contradict Newton within that domain, then Newton must be correct within that domain, and so there can be no objection to continuing to use Newton within that domain even if it's been falsified elsewhere.
In short: Once a theory is empirically tested, those tests don't just up and vanish when the next theory comes along. So long as we stay within the boundaries of those test conditions, our original theory is more or less guaranteed to be correct no matter how science develops in the future, unless we discover that those initial tests were somehow flawed or improperly conducted (as happened with N rays).
Continuing with our gravity example, it is widely believed that general relativity is incomplete, because it produces mathematical singularities under certain conditions, particularly when trying to describe black holes and the early universe. This does not invalidate general relativity when used to describe the rest of the universe, and it would still be valid even if we had a working theory of quantum gravity to replace it with.
So, to return to OP's question, if someone were to criticize a usage of general relativity on the grounds that GR is incomplete, it would not be unreasonable for us to ask what they want us to use instead of GR, particularly since there's no single widely accepted theory of quantum gravity. On the other hand, if we're trying to use GR in an area where it is specifically known to be incomplete, then perhaps that hypothetical person would have a point: you can't go around applying broken theories to situations they're known to handle poorly.