I'd probably walk up with the cash visibly in hand.
That or I'd just try to cool face it and act like "Oh, you know that ol' hunk of metal over there...I mean, I could use a grill.....Want a few bucks for it?"
I be just considerate and use honest approach. Go introduce yourself as a neighbor. Tell them you noticed that grill in the bush for awhile and was wondering if they use it at all. If not being used, tell them you would be interested and wanted to ask if they are willing to part with it. Who knows! They might just ask for $5 to take it away or give it to you for free because you asked and showed interest.
If they bring it out to show you, quickly asses if it is just old reg. SJ or Vintage SJ with wooden handles and 3 bottom vents. If it is latter, keep your cool and see what they want for it as you are just trying to help them get rid of it. If not, offer them what your are willing to pay. I would start low as this might be something that they are willing to get rid of anyways. I doubt it but If they say that it is used and stored in bush for convenience, no use going any further as good used SJ come up for sale fairly cheap anyways.
I would not go in with cash in hand offering as they might think they have something valuable and have negative results. At same time, I would not use second approach as it might have some sentimental value to them. They might get offended and get yourself kicked out.