Welcome to the Q&A Forum

The next time Google crawls the previously-linking page, it should note that the link is gone, as it will cache the page. Any benefit or detriment that the links was passing on should technically be nullified. Moz's crawl will update when it re-visits the page as well, but the frequency of Moz, Googlebot and the updating WMT is really hard to predict. If the link is on a highly-traffic, well linked-to page, G and Moz should pick it up quickly. If not, it can take a long time. The Moz index is updated about every 3 - 4 weeks; again, the removal of one individual link requires the latest crawl to have noticed that it has gone, which is likely but not a certainty.

I love that you made the tweet joke yourself. If you create this as your site (your site is the Pinterest looking site), you are hoping to maximize others linking to your site? I think it might drive good interest socially, but I am not sure that type of site lends itself well to links. If you do go with this type of site, I would focus your efforts on collections of pins and do promotions around those. I think that would be the best way to get link attention. Focus less on the pins and more on the boards. It's early Monday, so does that make sense?