1 - The most polite thing to do is to force feed yourself and stick it out. You don't want to be rude and even though you might not like what you're eating, you just force it down like bad medicine. This is the right thing to do but sometimes people hate certain ingredients SO much that it makes them gag.
2 - Chew it but then spit it out into the napkins. Yeah, you're probably going to get caught and there is only so much you can fit into that napkin. Plus if it's not disposable... what are you going to do with that napkin.
3- Fill up on side dishes. Fill up on the rice. Fill up on the mash potatoes. Fill up on veggies. Eat a very minimal amount of the main dish. It will look like you ate more than you actually did.
4 - Plead sickness. ie "I'm not hungry".. or "my stomach is bother me for some reason" .. now BE SURE you say this BEFORE they serve the food because you don't want to imply that their food made you sick.
5- Put it in your pockets, take it to the bathroom and flush it down the toilet. You need to be really sneaky about this. Nobody can see you stuffing the food in your pockets. If they you get caught, you're going to have a really difficult time explaining yourself. If you are
able to pull this off without anyone noticing, find a good time to excuse yourself and make a b-line to the b-room. Then you need to break up the food so that you don't stuff up the toilet. If you stuff up the toilet with the food that you supposedly "ate"... yeah that's the worst thing that could possibly happen.
TWO THINGS YOU SHOULD NEVER DO:
1- FEED IT TO THE DOG
2- SEE GIF BELOW