My old 70s Browning Hi-Power has developed minor rust along the backstrap - I think that is what it is called, it is the rearmost part of the grip that fits against your palm when gripping it. The rust is dark and seems to be many smaller-than-the-head-of-a-pin spots. Maybe 2 or 3% of the backstrap is affected. I keep oiling it and wiping it down, but don't know what else to do. Any suggestions?

Thanks in advance!

Get some #000 or #0000 (#0000...four "O"... is best, but may be difficult to find) steel wool from HD, Lowes or maybe a paint store, etc. and tear off a small piece. Put plenty of gun oil on the backstrap or the steel wool and go to it. It will remove the rust as well as "polish" the blue a little. You may be able to see bare metal afterward if the spots are pinhead-sized or larger, but it will get it off.

Do NOT substitute #00 or larger steel wool, as it will remove all the blue along with the rust.

I had the same trouble with my EAA Witness. I fixed it once and for all by refinishing the entire gun with the bake-on Teflon/Moly finish from Brownells.

If you prefer to keep guns in mint condition, like most do, that would bother you.
One option, as mentioned, is the fine steel wool but the problem most likely would show up again.
The other option, as mentioned, is refinishing...there are a lot of finishes to choose from.
You may find rubber grips that wrap around the backstrap to cover those "freckles" and stop it from getting any worse. A thin layer of grease or oil underneath the rubber should stop the rust cold.
Or just ignore it altogether, in time, even that bluing will wear off from honest hard useage, which does not affect the function.
It sounds like it was put away without oiling it up at one point in it's past, that's all it takes.

Many older HP's I've seen have had, at the least, light pitting in this area.  It tends to be pretty bad right under the rear edge of the grips.  If it's pitted, there's not much you can do short of having it polished out and refinished.  I would just try to keep oil on the area and keep an eye on it.  You could also try a good coat of paste wax instead of oil, wax stays put better and doesn't wear off quite as quickly.