Hmm, I see it now, Facebook is picking up both the donate button and the logo (and gives the user a choice, defaulting to the button).
The code is telling it to use https://www.hope-ct.org/site/wp-content/uploads/2013/05/hope-partnership-logo.png
, and that’s what Google+ uses. But for some reason Facebook isn’t obeying that. In fact, looking at the placement of both images, even if QuickShare didn’t explicitly specify the logo as the image, the Facebook parser should pick up the logo because of its placement in the header over the donate button’s placement in the sidebar.
It looks like even on a post that has an image, like https://www.hope-ct.org/hope-president-tony-lyons-and-vp-cal-price-appear-on-ct-style/, Facebook picks up both the post’s image (which QuickShare specifies as the canonical image for the page) and that donate button (defaulting to the image this time).
I suspect a bug in Facebook’s parser, since they use the same code as Google+, which is working as intended. It may have cached the donate button at some point and not cleared or something too. The only thing that you might be able to do to fix it is to re-upload the donate button and switch to the new one in your sidebar. The change in image url could help clear out that bug in Facebook’s parser cache.
The good news is that it looks like your site is doing everything correctly in its code, so any issues are with the external services and out of our control. So hopefully, things will get fixed on the other end at some point.