It is confusing as to what Google is doing here. If I click on the link to your form, I do not see the “Edit this Form” link. However, if I do the same with some of my own forms, I do see the link.
I thought it might have something to do with me being logged into Chrome but forcing a logout didn’t seem to make any difference. What is really odd is if I retrieve the URL using wget the “Edit this Link” text does not appear in the result nor does it appear in the returned content of wp_remote_get() which really has me stumped.
I am looking at the page on your site again and there is something very odd about it. There are two <style> sections which appear just before the DIV which holds the Google Form. One of the <style> sections holds a bunch of Google Forms CSS definitions which is already loaded in the document header do they’re redundant.
The second <style> tag is more concerning because it contains what appears to be a poorly formed shortcode which links to the “Edit Link” we’re chasing down.
Can you look at the source for the page where you have the Membership Form to verify there isn’t some rougue HTML in the page content? (Use the HTML editor view instead of the Visual Editor view).