I found a way to do it in Global Mapper. I import the xyz point cloud as an elevation grid, which it then creates a dtm from. Then I import the points that I surveyed, select them with the digitizer tool (edit...select all features with digitizer tool), and right click to get a function "Apply Elevations from Terrain Layers to Selected Feature(s)". GM then replaces the elevation attribute for all of the points I selected with the DTM derived value. I then file...export vector format...csv and I have a file that has the points with the dtm values. I load them into excel along with the original file, and I can see the differences.
Seems like this should be easy to do in Trimble Real Works software, but it isn't. At least it is not readily apparent.
It would be nice if it kept the old elevation as an attribute.