Three part feedback for you (did I get it, would I use it, how to market it).
First the "do I get it". Looking at your site with a "5 second look", I did not get it at first and probably would have bounced. I started reading "noun: the quality of.." first and found that distracting, next the call to action statement "Get Gratitude from your visitors" doesn't really tell me the how/why I'd want to give this a shot. I feel your statement in this post, "content was invaluable to me ... say thank you", is a better lead than you have on your site. But which audience is this site serving? Readers or blog authors? If it's blog authors than neither likely fit.
Taking a longer look at the site, I get what this is. The three columns below the primary CTA didn't make a lot of sense to me. When I read them I get it, but felt like the benefit could be told better. Also using the word Gratitude again felt confusing at first, the image is necessary to clarify that it's not some sort of credit, but it's saying thanks to the author for helping you out.
Going with your 3-steps approach perhaps something that is action oriented and highlights the benefit:
Step 1 - "Add the "Say Thanks" button to your great content"
Step 2 - Users "Say Thanks" directly to you right after you've helped them out.
Step 3 - You're now connected with your reader on Twitter and can start a conversation.
I'd also suggest you also ditch the columns. I read the column headers first, then started parsing. It added to the confusion of just what you were offering.
Overall I like the concept. But it feels like the audience you're reaching out to on your site is the readers of people's blogs who are looking to say thank you for content. But when I look at this I see it as a tool for authors to encourage readers to connect with them.
Would I use it? As a tool to connect to the readers of my blog, sure I'd give it a try. It's an interesting idea worth looking into. In a way it's like the SumoMe blog tools (which I use). As an author I want to engage with my users, if this leads them to finding them on twitter that's great. Most authors want readers to come back again, and getting them connected with you (via a newsletter, twitter, etc) is one of the primary ways engage with them.
As for marketing... When I think about what your product does (connect users to the author) it made me think of SumoMe, who's plugins drive users to signup for newsletters. Their model of marketing strikes me as usable for you (integrated into delivery of your service).
Hope this helps, let me know if you have questions.
PS: When looking to install the plugin I found the optional fields confusing. Just where is the Title showing? The button? Next to the button? It wasn't clear at first these fields were for one-use buttons.