Back where we've hunted for almost 40 years we've always had some sort of grill out and never put it away. And there's lots of bears out there - have seen as many as ten in one hunt. Have had a bear try to get at the hanging moose meat only once or twice, but have never had a bear get after the grill.
The only time it might be a problem is it depends on how the bears have been "trained". By that I mean you often get garbage bears that learn to get into the garbage cans all of the time. The only thing you can do with them then is either shoot them or transport them a long ways away.
Some campgrounds will have problems with bears. If they do, it's usually well posted to keep everything put away. If you're off boondocking where the bears aren't used to getting into trash, it shouldn't be a problem.
Bill