pluviosilla

ANSWER to my own question:

Just discovered a “developers'” area on Facebook whereThe theme was not conveying the information properly for some reason and, no, it wasn’t just a caching problem, because the problem persisted for over a week.

Two key things to note:
(1) Facebook has an indispensable tool for testing the display & appearance of logo & tag line in Facebook posts here:

https://developers.facebook.com/tools/debug/og/object/

(2) For me, the GT3 Eclipse Photo theme was completely unresponsive until I made a manual change to the header in the header.php file. I added these meta tag lines:

<meta property=”og:title” content=”We empower donors with choices and recipients by publishing needs and lifting the veil of their invisibility.” />
<meta property=”og:image” content=”http://targetedhelp.org/wp-content/uploads/2015/08/targetedhelp42-e1440874494697.gif&#8221; />
<meta property=”og:url” content=”http://targetedhelp.org&#8221; />

og:title tells Facebook what the tagline should be
og:image tells Facebook what logo image to display

The funny thing is that after including these, suddenly for the first time, Facebook started picking up the tagline information that the Eclipse Photo theme allows you to configure in these locations:

* Appearance => Customize
* Settings => General

Hope this gets you unstuck. I wasted almost a week on this.