OP, your kids are 13 and 15. They're old enough that they could understand it if you talk with them about this -- but they're also at ages where they very possibly won't care, or will tune you out, or if they just like all the food, they'll say, "Right, mom" and then do whatever the grandparents propose in terms of getting some Chinese food or whatever.....
Are the grandparents picking them up from school or activities, and then since they're all in the car, the car ends up in a drive-through? Can you find other transportation from school or activity back to where the grandparents await. That eliminates the immediate temptation to head for a drive-through.
Are the grandparents watching the kids at your house or at theirs? I wasn't quite clear on that but it sounds like it's at your house--?? If it's at their place, you need to change it to your own house, where at least you can know what's in the pantry (and can ensure you don't buy anything junky so it's not even in the house) and you know what you left in the fridge that day so you're aware if it's vanishing before dinner. If it's already at your place, and the issue is going out for food, you need to talk with the grandparents and say you're asking that the trips for food between school and dinner just stop altogether. Don't bring up their own obesity; they are adults and likely are more aware of it than you realize, so make it about "The kids' appetites for dinner seem to be affected, so I"m asking this of you." Then put specific snacks for after school/before dinner period in containers in the fridge, labeled if need be, and tell your kids that you're starting a new routine where that's what they eat.
At 15 and 13, the kids should have activities. If the grandparents are in OK health, are safe drivers, etc., what about ending the "looking after" arrangement and instead having the grandparents do things like take the kids to their activities after school once a week only, or join you and the kids for an outing on a weekend day once a month as well? Do your kids need someone to supervise? Is your older child able to do it, or do the kids bicker enough that you really want an adult around at times (I get that, it's the case with several friends' kids these ages--mature enough to be home alone but not to stay out of each others' space).
Start taking your kids with you to grocery shop and let them make choices. Start letting them cook and teach them about cooking healthy meals. Do not harp on their weight or their eating except to emphasize balance and a diet that isn't heavy in starches and sweets and fake junk in sodas etc. If they're kids who would be into this and enjoy it, try having one or both of them make a food budget for a month and decide how to spend it while sticking to some guidelines about vegetables and fruit etc.
Are both your boys in some kind of regular physical activity? If so, ramp it up if they're getting heavier, if you possibly can. If not, find something they like, anything. If there's a trusted coach or uncle or mentor they would listen to, have that person talk to them about the importance of staying healthy now so they don't have to fight for it later. But don't have this person let on that you're behind the talk or the boys will just hear mom's voice again.
But none of that has to do with grandma and grandpa. I would not make this about the grandparents, in front of the kids.
And please don't make this, as the saying goes, "the hill you die on." Yes, the grandparents are not good role models in terms of one thing -- eating habits. But they sought you out because they wanted to know your children, and you don't mention any other issues you have with them other than this one. Please don't cut them out of the kids' lives over just this. That would be an overreaction, truly, if they are being helpful and kind and model good behavior for your kids otherwise. There are things you can do, and changing the type of time the grandparents spend with the kids seems like one good route, but I wouldn't make this a do-or-die condition of their seeing your children.