You can buy simple gold (acid) testing kits,or make your own, a gold buyer will have these and could do the tests for you.
You can scratch the suspect bar on a stone and adding a drop of nitric acid to the scratch mark.
Most jewelers or gold buyers will use this or other tests with acids to dissolve base metals, any gold or less reactive metals involved in the scratch mark will remain.
The drop of nitric or (a drop of another acid combination of dilute to strong aqua regia testing solution) can be used along with a known karat of gold, by taking a known karat gold wire needle (or karat gold ring) making a scratch mark side by side on the slate stone, side by side with the scratch mark from the unknown suspect bar being tested, using acid (aqua regia testing solutions made of different strengths) to determine Karat or percentage of gold...
Sure some wells can have gold, and it is possible to have some gold in a filter, I just have a hard time seeing this much gold from a well or in a filter from a well.
I do not know what type or kind of well or what type of filter system is being discussed, so is it possible to be pumping gold with the water, yes is possible, being probable becomes more questionable and (most likely not likely), the density of gold would normally make it more difficult to pump gold than silt and sands...
with just a couple of pictures of what appears to me to be some gravel and sand, then seeing a large bar that looks to be brass or another yellow metal like gold, and from what I have seen from a couple of pictures so far it just seems fishy to me to be able to pull that much gold from a well, I would need a little more to go by before I can see it possible.
In some areas, beach sands and waves can concentrate gold. and that could make this a more likely scenario than pumping gold out of a well.
I would just like to know more, before becoming a believer.