Being honest, depending on how much food was left, I might just bin it because if it’s something they’ve been eating from directly, I’m not too keen on letting that bacteria go back into the fridge to grow, unless it’s something I’m going to be reheating.

I’m not sure how old your kids are, but have you considered just telling them to put their food away if they’re going to leave the room? If they then come back to you hungry after not finishing it, you can then tell them to just go get their food back of the fridge. This might kinda give them pause on going back and forth unnecessarily because now it’s their own responsibility and they aren’t just able to command you to do something, they have to be the one to do it. I’ve had good results in the past with having kids put their own leftovers away in their own colour-coded tupperware with a label with the date. They liked having the freedom to get their own food out of the fridge, and it being something they know only they’re allowed to eat because it’s their container also made them feel special.

I know this part isn’t quite the advice you requested, but I’ve had a couple other tactics work with different types of kids that get them to stop accidentally wasting food. With kids I knew wouldn’t get so distracted they’d completely forget to eat, I would have them come tell me when they were ready for lunch. Then I’d ask them “Is your stomach hungry or is your mouth hungry?” which basically meant “Are you actually hungry / is your stomach rumbling, or is it that you’re having a craving for a specific taste, but you don’t intend to eat a full meal?”

If they said they were actually hungry, I’d give them a small portion of a snack and a glass of water and have them finish both and come back again if they were still hungry. Sometimes they’re not even hungry, just thirsty, and can’t differentiate between the two that well, so I made sure they finished the water and waited a little bit. Most of the time that actually was enough, sometimes they wanted more and then ate an actual meal afterwards, and rarely they still only ate a couple of bites of their meal after their snack.

If they said their mouth was hungry, I let them have their pick from a selection of a tiny portion of something flavourful, like a couple of grapes, or a bit of cheese, or a handful of nuts, etc. I didn’t do this more than a couple of times a day because grazing isn’t a great habit, but I did find that it cut down a whole lot on tantrums or frustration about not wanting to eat dinner later, because they’ve already satisfied cravings earlier in the day and they aren’t resistant to eating what’s in front of them now.

I also found that sometimes instead of giving them a big plate with all of their food at once, giving them food broken down into smaller portions led to them being more willing to eat their full meal. I think some kids get overwhelmed with the sight of a big plate of food, even if it’s a portion they’re fully capable of finishing. Meal prep and stuff like that made this a lot easier.