It depends on how deluded (s)he is. If (s)he's really, really deluded, arguing is probably a waste of time. I wouldn't embelish the delusions either. I'd keep my distance!
My mate suffers from Delusional Disorder, Persecutory Type. The advice I've received from mental health professionals is not to contradict her delusions; she'll become defensive and resistant. Also do not agree with or participate in her delusions, as that only encourages them. They advise subtle reality-testing with her, but warn that delusional disorders are very intractable, and that's with long-term bonds of love and trust. In an adversarial relationship where trust is low to non-existent, I suspect that you're wasting your time.
32 years ago I was working as 2nd chef in the kitchen of the ABC ( the national broadcaster for Australia) located at Gore Hill, Sydney. The kitchen was run by a catering contractor. In retrospect the head chef was probably autistic. She certainly had an OCD as she would not stop interrupting me all day. When it came to making quiches she had no idea. The golden rule is when making quiche is to not put fork holes in the base. It was hard wired into her brain to put fork holes in the base. The egg/milk mixture would leek out on the supporting tray. So she tried using individual pie tins. Putting fork holes in the pastry base would cause the pastry to stick to the tin. So the job of making quiches was given over to me. When she saw me not putting fork holes in the pastry bases, she told me to put fork holes in the bases. I did not argue with her and did what she said to leave her deluded and less the wiser.
I recall a Buddhist abbot telling one of his monks when asked how to deal with the willfully ignorant that when you hear them talking bullshit to each other not to intervene but pretend you are watching a comedic act between two jesters.