Is there video of her entire check out process?
Was there clutter around the checkout station? The bags not placed correctly causing a lack of space placing the scanned items? Was there left over merch on the little stand where you put your stuff/basket pre-scan? Something that would cause distractions during the process?
She's not a trained cashier, and shouldn't be held to the standards of one. The video should most likely show no intent of stealing, and rather a mistake. This should have been easily rectified by security by allowing her to pay for the item.
Since she shops there frequently, (target app member? saved receipts?) it should show a pattern of proper behavior. This would show the isolated incident as an accident by an untrained operator. Does the $7 item that was missed part of a $100 purchase? More evidence that this is a training issue vs a premeditated theft.
Think like a lawyer, or better yet just get one. I hate leaving things to chance/good will of someone else in charge with something that can have a big negative affect me to long term. At least do some free consults with lawyers to get a feel of what might go down in court.
100% THIS!
From the information I have a normal RETAIL store has so much theft happening, people will just fill carts and baskets and walk out without paying for shit, security is NOT allowed to physically interfere and only record the incidents. (IDK how some of them even bother staying in Buisness, the rest of us a
definitely paying for that shit with higher prices I know theft loss is rolled into their pricing math it has to be)
Anyways here is what I would do step by step to get this to hopefully go away.
(
assuming there is NO previous record of any other forgetfulness 
)
Write a letter:
1. Present her previous shopping history at the store (Transaction Date and Amount from CC statements, over last 2 years probably)
no intent
2. Explain the lack of technology training and assistance to older customers from store staff
3. The lack of calibration of the scale for weight differences (IE the machine should have noticed the extra item but the resolution of the scale or the grace area for weight changes is too great to notice a small item)
4. She offered to pay for the item as soon as they noticed the discrepancy. (assuming here she hasn't even made it out of the store yet).
5. Politely explain to the store that if they want to press charges you will get a lawyer to do discovery on ALL of their prior losses in a time period so you can demonstrate this was accidental as opposed to intentional act (discovery for evidence of intentional acts at that location).
6. Perhaps a hint of calling to a local TV station to show aggression on the stores part of pursuing an honest-mistake-person, instead of helping them properly self checkout and chasing down larger theft at that location during the holiday season would all help this make it go away.
GL