This is just me but if I didn't have anything better to do and was one to just want to get out and detect, I would go ahead and systematically search the area that was pointed out. I would, maybe, look at the area and identify some high possibility areas to search. Like if there are any benches there, perhaps a shaded tree area, water fountain or what have you. Cover those types of areas especially well. Then, if you do get a call back, go search any specific area that might be mentioned. Like was mentioned, who knows what else you might find. Might find enough change or other jewelry to make it worth your while.
If I did find anything of special value, whether the ring in question or any other jewelry, I would take it and drop it at the park office or police for lost and found. I spoke to someone about a ring that I found and the suggestion was to photograph anything you find. Take it to a jeweler for an appraisal or professional discription. Keep that documentation along with a badge number and or name of whom you leave it with. Make sure you leave your name and phone number. In most cases, if not claimed in a time frame, usually specified by law or ordinance.... etc., the found objects are returned to the finder. Hopefully, then, if nobody claims anything you find, you will get it back yourself.
I, basically, detect for the fun of getting out and detecting. I am not looking for anything particular and, for me, the beer caps on the the beach are just as interesting and telling about the culture etc., around here and thus valuable, as the rings and stuff that I might find. Of course nothing can beat finding a nice gold and diamond ring but of all the stuff that I have found, I have found only one such ring. I have found a couple of common earings and another hand made bronze ring, but, most of what I find are common coins, bottle caps, nails, pull tabs, toys, wire... The most interesting items, other than the jewelry, that I have found, are a drain plug from a boat, a couple of foriegn coins, some diecast cars, a chunk of concrete with some rebar in it. I also find it interesting how the finds differ in some areas compared to others. Park play lots seem to be pretty free of trash and have a lot of coins, some childrens jewelry, zipper pulls from jackets and toys. One school play lot that I searched has similar coins and zipper pulls but add in paper clips and the eraser ends from pencils. Then, the beach is full of coins and pull tabs, beer caps, nails and lots of trash.
I have only just started with hard land like my back yard. I look forward to doing more because it seems very unpredictable what one can find. I had our area pegged as boring and not likely to yield much of anything as it isn't particulary old, was farm land before the subdivision was laid out etc. However in about an hour of searching, I found a few coins and a key chain that date to since we have lived here, I found a metal tag for a variety of rose bush, probably from the previous owners who had a rose garden in the middle of the yard, an old garden nozzle for the hose and some building materials, probably from when the house was built. Then there was a 1928 45cal bullet that I dug up. In tact with the slug in the shell. Anyway, there is so much to be learned and discovered through metal detecting. Sometimes the prize is the history and information that can be found and the objects are just the evidance that leads to that understanding. So, I would just say go search anyways. You never know what you might find.