No, no, no! Don't even think about using muriatic acid. That stuff is for swimming pools! This is not to mention how dangerous it is to your organs, and indoor electronics, etc.
You need a degreaser not an acid to break up the stain. Acids will dissolve cementitious materials, such as grout. I've seen grout dissolved down to the thinset from its improper usage.
Since your grout is so porous, you'll need to make or use a poultice. You could first try several layers of folded paper towel (white non print) and lacquer thinner. Soak the paper towels (approx. 6-8 layers/folds) with lacquer thinner. Cover with plastic, and tape down the perimeter edges. Allow to sit overnight, remove the plastic and tape in the morning. Allow the paper towel to dry thoroughly (no peeking). Remove the paper towel after it's dry.
Report back with your results.