Dump a gallon of chlorine (bleach) down the well and see if that don't help, let it set overnight, pump it till the smell of bleach is gone.
It is a closed well... Just a pipe with a pump attached... There is now way to get into it. I am wondering id it could be sulfer.. But i would think that would smell like eggs...
Even a closed well can be open, it may take some tools you don't have but it has to have a way so if you need to pull the pump.
I had a well like this that had sulfur and it did smell like eggs, if the walter had sat overnight.
Yes, i can remove the pump housing, but it is still just a pipe.. No open hole. Just one 3.25 inch pipe.
If you don't think it's sulfur, dump the bleach in the 3.25" pipe it is a good thing to sanitize the well every few years anyway.
The open hole will be at the bottom of the 3.25" casing.