My impression is that screenshots don't mean anything to them. They don't help find find the rate themselves, and they don't consider it sufficient proof that the rate is still bookable.

So I never bother with screenshots.

Instead, I don't give just the website. I give step-by-step instructions on how to look up the rate. For example, at one site, I noticed that one some days it doesn't find the hotel "by locaiton", but it has a "search fby hotel name" feature, and that always works. So I explained to the LNF team (in the comments fields) how to do the search that way. Next, thiis site shuffles the name of the hotel around, and so it doesn't show up alphabetically where someone (who knows the correct name of the hotel) might expect. So, again, I explain this in the comments. THen the site gives dates in a European format (day/month). Again, I explian this in the comments. Then the site has confusing cancellation terms, so I just simplify and explain that the site's rates are refundable (they are) just like at marrott.com. (That seems to make them gloss over a maybe slighlty different cut-off date for refundable cancellations.) At other sties where the terms are hard to find, I explain how to click what to get to the terms.

Ie, I never expect the site name alone to be enough for the LNF foks, and I don't think screenshots of the final rate display help a single bit. But I guide them along so that if they follow the instructions they cannot possibly fail to find the rate. And it seems to work every time (except, of course, if I use a third-party site where the rate really can disappear very quickly).