Does Fixing Photo Metadata Reduce Image Quality?
No. Writing a date changes the metadata block, not the picture. Here is the one setting that does re-encode.
No. Writing a date or a location changes a small block of text inside the file. The picture data is not touched, not re-saved, and not compressed again.
This matters because a tool that re-encodes your images to change their metadata would cost you quality every time you ran it. This one does not. Your JPEG stays the exact same JPEG, byte for byte, apart from the metadata.
The one exception is conversion, and it is optional. Turning HEIC into JPG genuinely rebuilds the image, because those are different formats. Same for converting an old video. Both are switches you choose to turn on, and both are off if all you want is correct dates.
So run it on your whole library without worrying. If you only want dates and locations fixed, leave the conversion switches alone and nothing about your pictures changes. The first 500 photos are free.