Oddly enough, for things like this I have been using Woodland Scenics Foam Tack Glue.
You need something that will stick to slippery surfaces, will remain flexible, and won't show. (Canopy glue may also fill the bill, as people have noted).
I would also use Walthers Goo, and it would do a superb job, but you have to be really careful not to let the ugly brown glue show in an application like a grill. Goo is hard to manage and work with in tiny areas. It can be done, but the Foam Tack Glue seems to have similar properties of flexibility and adhering to slippery surfaces, with the added bonus that it dries clear. I bet some tiny dots of it all along the backside on the edges of the grill would hold it very well and would not show.