Facebook app uses a lot of data storage while not logged in
I've heard from various sources that Facebook (and other companies, frankly) do track geo-locations for various purposes, the first and foremost being that they want to serve you ads that you usually see around the web. I've also seen that they really do snoop around a lot (on all of your devices, and yes, even without an account), so geo-locations are probably just the tip of the iceberg. 

You might want to check your privacy settings for Facebook just to see what data is being collected. If you're tired of Facebook eating up the storage on your mom's phone, uninstalling should take care of that. Of course, if you want your mom to be out of Facebook's peering eyes, good luck, because you really can never escape Facebook trackers unless you suspend yourself from technology.

Hope this helped.