Surely, the title they were looking for is "Blood Ties".

Or maybe they were going for a fatherly tone. Ties are something one gets a father, and there's also blood because of the situation.

Perhaps 'Ties' refers to all the relationships the father could not get away from - could not "untie" - like the one with Shim, even though they weren't related by blood.

Really, all the main characters had hidden or unexpected ties to other characters that were revealed slowly throughout the movie. In other cases, the ties we thought existed between characters turned out to be false. If you think of it that way, the title, "Blood and Ties" makes more sense.

I think bloody ties fit better.