How do I convince her family I'm different?

I'm 16 and her, her friends, and I became good friends. This particular girl is known to have met some scumbag guys online and her mom knows that. So, me and this girl just admitted that we had a big thing for each other, and the next day (today), I get texts from this girl's grandma and her mom threatening cops because "felonies can still be committed between states" (we live in adjacent states). Her mom texted me saying that she heard I was mean to her daughter and that I'm no friend of hers (when she asked who the number was I said it was ____'s friend _____). She was saying she saw all the perverted messages (which I know nothing of, so they're not me) and she will call the cops if I don't lose her daughter's phone number (and she blocked my number from daughter's phone). Meanwhile, this girl and her friends say that they've said nothing but nice things about me to anyone. So I don't know what I should do... Should I just let it go even though I really care about her?