That lanyard ring base or what ever it is, can't really tell in the picks could have been simply soldered into place.
Most plating will cover soft solder because of the tin content in the solder.
Hard solder will plate perfectly too as will braze. But they require much higher heat, the latter nearing weld temps.
Anyway, that area behind it sure looks like it was filed down quite low before plating. That's judging by the grip fit being above the metal even as worn as they are.
I know that labs can sometimes recover a stamped image like a ser# from a surface that been ground out or filed a way quite deeply. But it all depends on how much force was applied in the strike to make the orig marks,,the compression of the metal.
If you want to try,, I'd go ahead and mechanically remove the nickel from the butt area,,that means polish it right off with grit paper backed up on a file to keep things a flat as possible.
They aren't too flat to begin with, but you'll soon see where you need to work and where not to.
I can just about guarantee there's no number under that plating,,filled in or otherwise,,visible.
All you will find and all you need to dig down to is clean steel in the area that the ser# is supposed to be in.
What you may find is not clean steel,,but a combination of filler in the steel. That being hard solder or braze used to fill grinder hollows or rough file marks when a # was removed.
The ser# may have been right in the middle of the butt,,not off center to the rear where the hollowed out area is. If that added base has a shank that required a drilled hole through the butt,,then there went for eternity part (at least) of the ser#.
If the ser# was all in that hollowed out area and there is just clean steel under that plating (and you won't know till you polish it away),,then there is a slight chance home brew acid lift methods will faintly make it reappear for you.
With all that, there's that nagging issue of Altered, removed, obliterated ser#'s on firearms.
The #3 is considered an Antique Status firearm I think no matter the ser#,,so does that remove that issue?
I don't know the answer.
Then what does the State of Michigan think of the handgun w/it's ser# removed.
Just asking cause I really don't know.
I'd like to see the oldie fixed up again