She still lives alone and is completely cognizant about everything else in her life. Can talk about current events, has good memory etc. In the evenings though, she says a "gang" is operating around her place. They put wires on the roof, take pictures of her through the windows and put white powder all over everything inside and outside her home. She gets mad if you try to use reason and logic to show her that there is nothing there. Absolutely believes these "gremlins" are there but mind seems fine otherwise. We are not sure what to do with her?
Your situation sounds a great deal like my situation with my mother 2 years ago - she could still drive, but thought she was being robbed nightly and was constantly wanting to call the police. If it turns out this 88 year old female has dementia or Alzheimer's, it is important to get her legal papers in order immediately. Someone will need both medical and financial POA to be able to take care of her.
There is a free book you can read on the internet about this called "Understanding the Dementia Experience" by Jennifer Ghent-Fuller. I recommend you read this as it will explain to you how to talk to someone with dementia/Alz. It also explains the arc of the disease and the prognosis. It is painful to read, especially, if this 88 year old female is a relative of yours, but it is better to know what is going on and what will happen and how to work with her, than not know. Likely this woman could benefit from medication to calm her agitation and hallucinations such as Risperdone. Talk to her doctor about this - but not in front of her.