That was talking about how Parker is pretending everything is fine and doesn't want Walter to learn the truth of the past ever. He did something so terrible that he doesn't feel regret for lying to Walter. I think this big mistake that he doesn't want anyone else to make is actually related to his treatment of Gil (and Tora). His declaration that he won't let the other love interests hurt Walter again is giving me potential yandere vibes.
Parker is cockblocking Gil, and an obscure choice on Gil's route reveals that Gil's still a virgin because of Parker. He tries to stop Gil and Lars when he mistakenly believes they're fucking in the restroom (Lars is puking instead) but Liz stops him. Remember on Parker day 7 when Liz talks to Walter about Parker's cockblocking of Gil? She mentions overhearing Parker talking to himself about there being a terrible mistake he made that he can't let anyone else make. When Gil talks to Walter about it, he explains that Parker means well and that Parker's there to stop him from making the same mistake. If only Liz brought it up about that, she could easily have misinterpreted, but Gil also brings it up in conjunction with the cockblocking. The only serious thing Parker repeatedly goes out of his way to stop people from doing is unwanted sexual advances. On Lars day 8 if you go to the hot spring with Parker but don't play along with Tora, Tora suggestively backs Walter into the wall and Parker hits Tora out of reflex.
Though just to clarify, some of the virgin thing probably wasn't intentional, more that Parker needing Gil's help was why Gil cancelled his plans to sleep with Lars the night of Episode Lars. That was probably also the night Liz put out a missing person's report on Parker. Though this begs the question why they never slept together while they were dating, and Lars never found out that Gil was a virgin until Gil day 7.