If I understand correctly, the issue here is really that the "Website" cards are ugly and probably shouldn't be linked to so prominently - certainly not until they're beautified, but possibly ever.
I believe we're no longer using the modal window seen in this screenshot, but the new source listing (which you can expand on the right side of the page) has the same issue. For a given source, you can click on the Website, the Source title, the author, or the original link. Three of these are fairly clear: the source title takes you to the source page on wikirate, the author to the user's page, the original link to the original (external) page. But the "website" is less obvious; it takes you to a card for that website, which includes all the sources from that website on wikirate.org.
We can make that page more attractive, but I think it would be confusing to link to that card from here anyway. I'll suggest that we make both the website and the title link to the source page.
Re "if I understand correctly"...I didn't. The problem actually has to do with bad data in some old sources, specifically the website field. If I understand things correctly *now*, then this shouldn't happen with new sources. Fix for old sources coming soon.
These should all be fixed now.