The TI-84 Plus CE has a piece of clear plastic in front of the LCD so the LCD is very unlikely to be damaged. They most likely are attempting to clean the plastic screen protector. :)
The screen protector will get microscratches on its own from just being inside a bag with any dirt. Also, there will be unavoidable 1 cm long vertical marks on both sides of the screen where the slide case rubs. I highly doubt the qtip caused any noticeable scratches. Unfortunately I don't have any tips on how to repair them.
Unfortunately, neither replacement LCDs nor screen protectors are sold separately. They have to be salvaged from a donor calculator.