Yes. You want to keep whatever is left of the frenulum: you don't want to try and remove it or ask anyone else to remove it. That part of your penis is still important, even without the foreskin. It plays a part in erection and also in sensation. Without it, you'd typically have less sensation.
There's nothing weird about it (there's also nothing weird about a foreskin!), it's a part of everyone's penis.
Never doubt that a small group of thoughtful, committed citizens can change the world. Indeed, it is the only thing that ever has. - Margaret Mead