If that was unavoidable, you'd see thousands of people on the streets of the five boroughs walking around with grease all over their arms and pants. Hilarious image.
I hate to say it, but it doesn’t seem like you’re very aware.
I grew up eating this greasy stuff; you either dab the grease off with a napkin or fold it and let it drip on the plate.
You don’t do what you described unless you’re unaware that it’s going to happen. If you indeed ruined many a shirt this way, you are so incredibly unaware that I stand aghast at your unawareness.