I Agree with Tim, Then I would scrape and sand to level out the infected area. wipe with a pre paint cleaner of alcohol, and the apply a nice even coat of POR-15, let that dry inspect the finish to be sure you have complete coverage then apply a color top coat of your choice.
I would do the same for any mating surfaces that may or do have rust, once you are happy that all areas have been treated reassemble grill and enjoy it for many, many more years as the rust will return tin the protected Areas.
Google POR-15 to read up on its history, can be purchased at several sites including of course Amazon.
Hint lay down a drop cloth on surfaces you do not want this to stain, and wear protective gloves, and old clothes you do no mind staining, as once this is on a surface it is a bear to get off, like your hands can take over a week of hard brushing to remove, skin leaves faeter.