What is the ruling on dealing with a mother afflicted with dementia who accuses her granddaughter of theft and insists on it, while the children know that these are false statements?

It is your mother’s right upon you that you treat her with piety and kindness, especially since she has reached old age, as Allah Almighty said: "And your Lord has decreed that you not worship except Him, and to parents, good treatment. Whether one or both of them reach old age [while with you], say not to them [uff] and do not repel them but speak to them a noble word." Part of piety is to be patient with her and beware of showing annoyance, lest it lead to disobedience. If your mother has dementia and has lost her mental faculties, she is not held accountable due to her loss of legal capacity, as stated in the Hadith: "The pen is lifted from three: from the sleeper until he awakens, from the child until he reaches puberty, and from the insane person until he regains his sanity." Discussing with her her accusation of her granddaughter stealing is futile and may be counterproductive.