Thanks.
The DEM is an img file, not a tiff. Not sure how I'd convert that to something editable, but I'd rather not anyway because it is part of a matrix of 50+ DEM files that have been tiled to create a large-scale scene. The artifacts aren't no-data areas – I did check that. The good news is that they are in the background. I am saving out the combined DEMs as a ter heightfield file, and found that if the resolution is reduced most of the artifacts average out. So problem solved this time.
I guess I was hoping there might be a procedural way to fix things like this, but understand why there isn't.