How are you making the comparison? A couple of years ago Google shut down the API by which SketchUp had been getting images and terrain and Trimble was forced to seek other sources for geolocation data. So, you can’t actually be comparing with Google Earth inside SketchUp.
I don’t know the spatial resolution or claimed accuracy of terrain height in these new sources, but that could contribute to a mismatch with the GPS data. It would be interesting to choose a location on the terrain in SketchUp, measure the altitude there in the model, and then take your phone’s GPS to the same location and see whether they agree. If they differ, it would be possible to project the track onto the terrain in SketchUp if that matters more to you than GPS accuracy.
A more technical possibility for the difference could be if the terrain data is height above sea level whereas GPS is height above the WGS 84 reference ellipsoid. That could happen if the new source is getting heights from a traditional map (which would be above sea level).