You may be able to scrape some of it off, especially if you jump on it before it cures (a long process that starts with setting. If there's a sealer or release agent on the stamped concrete, so much the better.

A small cold chisel, wire brush, Dremel tool would be good starting places. If they can get dinosaur skeletons out of stone, you can do this.

Admittedly, it would take a steady hand and some finesse, but I'd be inclined to take a light-handed, electric grinder to it -- carefully adhering to the pattern as much as possible. I've had to do that to my own concrete work before and it came out as passable.

A second option comes to mind: with a chisel, clean up anything that exceeds 1 1/2" limit (or whatever dimension you determine) from bottom of cap. Using a thin board as a straight edge and temporary support for the bottom edge of a bead of mortar, (The boards thickness determines the mortar's thickness.) Apply a straight, flat, 1 1/2" band band of mortar (which will appear as a bottom part of the bullnose cap) to just below the cap. (There are lots of Youtube videos of Chinese/Asian masons using the technique of mortaring against temporary, handheld guides & templates.)

That's an awesome suggestion, Yaardvark. I had actually been looking at running a 2" band of teak or mahogany lath over the mortar, but that would create a couple of other challenges to handle. The method you suggest is much more subtle.

I'm going to start with tatt's suggestion, since I have those tools at hand. I might even wear my Panama Jack hat while I'm doing it and channel Dr. Alan Grant.