This is what they can do and yes I'm borrowing a bit from Blade Runner:
1. Rey is Luke's daughter raised in the ways of the Force by Luke himself since birth.
2. This makes her stronger in the Force than Ben Solo who became Luke's pupil at a much older age.
3. Ben turned to the Dark Side and slaughtered all the other students except Rey.
4. Fearing for her life Luke used the Force to give her amnesia and replaced her memories with a fake childhood of growing up on Jakku when in reality she was sent there as a fully capable adult and kept under the watchful eye of Luke's trusted ally Max Von Sydow.
5. So that his secret could be kept hidden he not only changed Rey's memories but he erased Kylo Ren's memory of her as well as his own memories of his daughter. Only Max Von Sydow and possibly Leia know the truth. This would not only tie in with Luke closing himself off from the Force in TLJ (and thus not dismissing Rian's film) but it would also play off his failure in ROTJ to adequately hide his thoughts of his relationship to Leia from Vader. Knowing that Rey would be in danger as long as she was in his thoughts caused him to make the ultimate sacrifice and remove all knowledge of his daughter from his own mind. Again going back to Blade Runner when Deckard denied himself any link to his daughter's upbringing it was seen as a noble act of love and sacrifice.
6. Since Kylo Ren and Rey were tapping into her created memories they both wrongly believed that she was raised by nobodies which again was for her protection.
Issues that this would resolve:
1. It would explain why her mind went ape**** in TFA when she touched her father's saber with it being the first object that the two of them interacted with since her exile. Her mind was assaulted with images, some real, some implanted, all at once as her subconscious tried to make sense of what was true and what wasn't.
2. It would completely explain why she's so insanely gifted in using the Force. Her subconscious mind remembers years of training while her conscious mind does not.
3. It could explain why Han was so quick to make her a part of his crew, if she was erased from his mind then maybe a part of him felt a strange connection to her that he couldn't place. Maybe he even showed her and Ben how to fly the Falcon when they were kids (which causes yet more of her skills to be explained.)
4. It would make Snoke's line in TLJ more poetic in that he believed that he "wrongly" assumed that Skywalker would rise to face Kylo Ren when in fact he was correct. He just didn't know that there was another Skywalker which again ties back to themes from the OT up to and including Yoda showing up one last time to make sure that the one remaining Skywalker isn't lost forever.
This could all come to light in Episode IX even bring Luke back as a ghost (with all of his memories of his daughter restored) and worst case scenario have him do an exposition dump a la Ben on Dagobah in ROTJ bringing Rey up to speed on what happened. He can even be one of those fancy new ghosts that can touch living people and give his daughter a big hug, show everyone that he was always an awesome hero and that part of him going to the island to burn everything was an unforeseen byproduct of the "new" fragmented Luke that he became when he purged his own memories.
Maybe say that 5-10 years pass between TLJ and Episode IX and in that time Rey started to lose hope and didn't hone her skills while Kylo used that time to rigorously train and surpass her (in order to make their final confrontation more dramatic and satisfying.)
But after learning the truth from Luke he unlocks the rest of her memories and she gets to face Kylo (who is still stronger even with her memories restored) and kick ass and give ultimate victory to the Good Side once again, with the ghost of Luke beaming with pride and him being the badass with the master plan that came to fruition and once again the hero that everyone always knew him to be.