I did some testing, and I think I understand it. In all situations, picking the first option, to overwrite all metadata worked and both images were downloaded. But I'd prefer not redownloading my entire background library each time a new one is submited
I did as you said, unlinked a game with no background from database, then used the search button to link it again, I tried to scrape both that game, and a game that already had a background at once. No images were downloaded.
Then I tried scraping two games that both didn't have a background, that worked fine, and backgrounds for both games were downloaded. From that, I presumed that Launchbox tries to scrape the first game, detects it already has a background, and downloads nothing. From that point onward, it doesn't download any more backgrounds as it's already decided not to for the first game, so I guess it doesn't even check the other games afterwards. I did one more test for that.
I scraped three games at the same time in alphabetical order, the first didn't have a background, the second did, and the third didn't. As expected, the first game downloaded a background, the second was skipped as it already had one, and because of that it continued skipping games afterwards and didn't download a background for the last game. Is this a bug I should report, or intended behaviour?