OK, I think I've found the problem and it's strange.
But first, it's important to know that these invaders (which is what I'm calling them -- they remind me of old Space Invaders sprites) didn't appear until the foliage was added to the scene. Then they showed up in every render, but in different locations each time. Sometimes over foliage, sometimes over water or elsewhere. (I even rendered the same file on both machines last night and yep, they showed up in both.)
While loading the file I finally noticed this error. It was getting thrown each time TG attempted to load a displacement file associated with one of the trees:
FreeImage error: Warning: loading color model R as Y color modelSo I looked at the file, which came with a Megascans bark shader. It was an EXR file and had a single channel (which appears in Photoshop's layers panel) named "[R]". All other EXR files in the scene have a single channel named "RGB".
FreeImage must be the library module that TG uses for EXR support. This page explains the problem:
https://sourceforge.net/p/freeimage/bugs/283/. More detail here:
https://github.com/imageio/imageio/issues/356.
Anyway. I just changed the channel name in Photoshop from "[R]" to "RGB" and resaved it. The error went away and (fingers crossed) the render currently running looks fine so far. Why this would have anything to do with the renderer is beyond me. But the problem seems to be fixed: No more invaders. I'll be doing nightly renderings so if it hasn't been fixed, it will show up again soon enough.