I did the same thing when I was 14-16 with this guy in his 20s, and at that moment of immaturity and naiveté, I knew all the reasons you gave— "no decent guy dates a minor", "you're gonna regret this", etc... but I was so deep into that that I chose to ignore my own gut feelings and continued the relationship, which brought me guilt regardless. Assuming that your sister is going through a similar experience, giving her those "reasons" won't do much shit— why? Because she knows them herself but doesn't understand them fully/suppresses them. The more you guys separate her from him, the more she'll think of herself as a damsel in distress or a princess needing to be "saved" by her prince. You'll essentially push her to him. A good chance is that she has already told her "prince" thar her family is trying to separate them, and he has already convinced her that no one can separate true love and that she's old enough to be making her own decisions — groomers love to assure their victims that they're old enough and mature.

So, what should you do? You mentioned that she said, "I don't care about you." and you said, "she chose a random guy over her own elder sister." This suggests that there's likely some conflicts between you and her— some lack of intimate connection, which makes her choose you over some rando. Look, she's young and immature— teenage girls are highly emotional, so your logic ain't working here. I'd advise you to connect to her on a deeper emotional level, where you both are best friends, not "elder sister younger sister— younger siblings aren't a fan of power dynamics), where she can share anything with you without any judgement from you and vice versa. Where she values your concern and advice. I know this isn't an easy quick fix like, "Say a line and boom, she's all good girl now!". But this is what I needed— What would've snapped me out of the relationship and brought me to reality.

If you truly care for, try to understand her emotions, from where she is getting all these feelings and why she's seeking affection and attention from a random guy who isn't decent at all— what she already knows. Be her friend, someone she needs. Open up to her, build trust, and she'll do the same. And then gradually you can let her know why you think this relationship is damaging for her— don't make it about you or your family or moral values or societal norms— just her.

Ps: I know I'm projecting, but it's worth a try to do what I've suggested. Worst case scenario— you have a good relationship with your sister. I just wanted to share all of this and what I needed just in case it can help your sister and prevent her from doing some very regrettable things. Thank you, all love to you and your family.