I'm assuming that she's either reached the point at which she can't be convinced they're not real, or she's heading in that direction.
I like the cup of tea idea and indeed anything that would distract her.
Another thing you can do is to come up with an explanation that's not about them not being real. Do you have a cleaner/paid caregiver/visiting relative she could be indirectly reminded of?
"I saw her going through my things."
"I saw Jane rummaging all over the place earlier for a clean hankie."
Or could you convince her it was you?
"I saw her going through my things."
"I've just been tidying your drawers."
With Dad, I've also rammed home the idea that some things in particular disorientate him. A lot of the time I respond to things like this with "have you just woken up, Dad?" I reckon there's a good 70-80% chance he has or thinks he has. "You sleep very heavily when you take a nap these days and I've noticed for some time that quite often you wake suddenly in the middle of a dream. I do that sometimes and it's very disorientating. The dream seems very real."
It really seems to help. It's far easier for any of us to accept that the person we just saw wasn't there if we think we were dreaming/half asleep than if we think our mind is playing tricks on us or if, as Dad sees it, he's going gaga/mad. (I really hope that as time goes by, however frightening the symptoms of dementia may be, people will gradually be less frightened of being seen as 'mad'.)