How can I get rid of the orange stains in toilet from well water?

CLR full strength should do it.

CLR agreed.

I soak my commode with a cup of vinegar each week to remove all minerals from the water. Then use a brush to get it off. I also have Mr. Clean toilet bowl scrubbers. They work like magic if I have been gone out of town and the stain is really set in. They are expensive, so I only use them when I am done with the vinegar and brush treatment. Between the two, the bowls are mineral and rust stain free!

Stains will continue without adding a filter system to your well.

I use Simple Green. Works great on my rusty well water stains

I would try The Works cleaner that I get at our dollar store. It works great.