A recent article in the New York Tmes by Tim Herrera is titled "Let Go of Your Grudges. They're Doing You No Good."
It starts out:

One of my favorite party games is to ask a group of people this simple question: What is your oldest or most cherished grudge?

Without fail, every person unloads with shockingly specific, intimate detail about their grudge. Career slights (intentional or not), offhand-yet-cutting remarks, bitter friendship dissolutions; nothing is too small or petty when it comes to grudges.

The gist of the article is that holding a grudge is destructive to the person holding it, and it doesn't harm the person it's held against. The scientific community has shown this conclusively. The article gives you steps on how to let go of the grudge and forgive the person.

There's a different perspective on why it's important to let go of a grudge and forgive: