If he were having happy delusions, I'd be fine with that, but he keeps saying that there's some woman with several children that he has somehow wronged and they're going to come and hurt him unless we give her money.
I certainly don't want to agree with him. Any suggestions?
This sounds exactly like Lewy Body Dementia rather than standard anxiety. In LBD, visual spatial issues create the hallucination (the woman at the window), and frontal lobe damage creates a 'story' to explain it (owing her money).
Treating this as basic anxiety with standard sedatives can be dangerous for LBD patients. Instead, try environmental fixes like drawing the curtains to break the visual anchor, and use 'therapeutic fibbing' to resolve the guilt such as “I paid her, she is happy and went home”. If it continues, they need to see a neurologist who understands cholinesterase inhibitors, not just an anxiety script.
Remember that temporary peace is victory. If you try to make him deny seeing her, he will lose trust in you.