Are you starving or otherwise in poverty to where this would be one of the only things you get to eat?
Outside of those circumstances, I wouldn't do it. For two reasons. To me, it's no longer 'food'. It's the equivalent of eating bark or sawdust, so it doesn't matter to me that it's going in the trash. The waste was created when the animal was slaughtered in the first place.
Even if you don't have that perspective, this creates a weird dynamic where it expresses to other people that you're okay with all of it as long as its 'extra'. Meaning a family member might intentionally save some for you, knowing you'll eat it, because they think you'll starve otherwise.
Maybe they'll buy extra portions of food the next time they get takeout with this same intent. Not necessarily out of ill intent to say "see, you're not vegan", but more like "I'm worried X isn't getting enough protein, so I always get an extra chicken wing and say I can't finish it".
In short, it's their problem, and you choosing to eat it only has potential downsides outside of the dire circumstances I mentioned.

