I downloaded the exiftool and think I correctly tried to add a comment with a "file updated" message in response. However, when investigating the file with File Explorer, the comment was not added.
Windows doesn't read the
Comment tag in jpegs. It's a pretty fragile and useless tag and gets overwritten frequently by various software. To get something to show up in the Windows property "Comment", you need to write to either
EXIF:UserComment,
XMP:UserComment, or
EXIF:XPComment. See
this post for the full list of tags<->Windows properties relationships.
Take note of the fact that these tags have very little support in software other than Windows. A better place to put information would be in something like the
XMP:Description tag, which Windows inappropriately calls "Title".
It's up to you if you want to continue "fixing" your jpegs that way, but understand that when you resave a jpeg like that, it degrades the image quality.
I would suggest trying a this to fix the jpgs. Install
irfanview and install the
plugin pack. The plugin pack contains a plugin for lossless jpeg functions. Load up an offending jpeg and select Options Menu -> Jpeg Lossless rotation. You can then set it like this example and it will rewrite the jpeg without losing any data. Hopefully, after that, Windows will be able to read/write the file correctly.

If it works, you can then do this to all your jpegs in bulk by hitting the File Menu -> Thumbnails to select all the images you want to process.